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## Grigorchuk, Rostislav Ivanovich

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 Author ID: grigorchuk.rostislav-i Published as: Grigorchuk, R. I.; Grigorchuk, Rostislav; Grigorchuk, Rostislav I.; Grigorchuk, R.; Grigorchuk, Rostislav Ivanovich; Grygorchuk, R. I.; Grigorchuk, Rotislav I.; Grigorchuk, Rostyslav; Grigorchuk, Rotislav Homepage: http://www.math.tamu.edu/~grigorch/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 147 Publications since 1977, including 6 Books Biographic References: 6 Publications
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#### Co-Authors

 41 single-authored 12 Nekrashevych, Volodymyr V. 8 de la Harpe, Pierre 8 Kurchanov, Pavel F. 8 Nagnibeda, Tatiana 8 Savchuk, Dmytro M. 7 Bartholdi, Laurent 7 Šunić, Zoran 7 Żuk, Andrzej 5 Benli, Mustafa Gökhan 5 Kravchenko, Rostyslav V. 5 Stepin, Anatolii Mikhailovich 5 Wilson, John Stuart 4 Dudko, Artem 4 Muntyan, Yevgen 4 Sushchans’kyĭ, Vitaliĭ Ivanovych 3 Bondarenko, Ievgen V. 3 Bowen, Lewis Phylip 3 Ceccherini-Silberstein, Tullio G. 3 Lenz, Daniel H. 3 Ol’shanskiĭ, Aleksandr Yur’evich 3 Šuniḱ, Zoran 2 Andriĭchuk, Vasyl’ Ivanovych 2 Drozd, Yuriĭ Anatoliĭovych 2 Futorny, Vyacheslav M. 2 Komarnytsky, M. Ya. 2 Kozlov, Valeriĭ Vasil’evich 2 Novikov, Sergeĭ Petrovich 2 Petravchuk, Anatolii P. 2 Petrichkovich, Vasil’ Mikhaĭlovich 2 Shestakov, Ivan Pavlovich 2 Shumyatsky, Pavel 2 Sinaĭ, Yakov Grigor’evich 2 Vorobets, Yaroslav 2 Zieschang, Heiner 1 Allums, Derek J. 1 Anosov, Dmitriĭ Viktorovich 1 Artamonov, Vyacheslav Aleksandrovich 1 Artemovych, Orest Dem”yanovych 1 Aseev, Sergei M. 1 Babych, V”yacheslav Mykhaĭlovych 1 Banakh, Taras Onufrievich 1 Bezushchak, Oksana O. 1 Bokut, Leonid A. 1 Bolibrukh, Andreĭ Andreevich 1 Bondarenko, Vitalij M. 1 Bondarenko, Ye. V. 1 Bukhshtaber, Viktor Matveevich 1 Collins, Donald J. 1 Davydov, Alekseĭ Aleksandrovich 1 Delzant, Thomas 1 Dokuchaev, Mikhailo 1 Fomenko, Anatoliĭ Timofeevich 1 Ganiushkin, O. G. 1 Gavrylkiv, Volodymyr M. 1 Golod, Evgeniĭ Solomonovich 1 Gonchar, Andreĭ Aleksandrovich 1 Gorodnii, M. F. 1 Grigor’ev, Dmitriĭ Yur’evich 1 Grines, Vyacheslav Zigmundovich 1 Gubareni, Nadiya M. 1 Gudivok, P. M. 1 Gurevich, B. M. 1 Hanyushkin, O. H. 1 Herfort, Wolfgang N. 1 Ivanov, Sergei Vladimirovich 1 Kac, Victor G. 1 Kaimanovich, Vadim A. 1 Kashu, Alekseĭ Ivanovich 1 Katok, Anatole B. 1 Kemer, Aleksandr Robertovich 1 Kerr, David 1 Kharchenko, Vladislav K. 1 Kharlampovich, Olga G. 1 Kolesnikov, Pavel Sergeevich 1 Kolyada, Sergiǐ Fedorovych 1 Kravchenko, Rostislav 1 Krylyuk, Yaroslav S. 1 Kurdachenko, Leonid Andriĭovych 1 Kutateladze, Semën Samsonovich 1 Kyrychenko, V. M. 1 Kyrychenko, Volodymyr Vasyl’ovych 1 Latyshev, Viktor Nikolaevich 1 Leemann, Paul-Henry 1 Leksin, Vladimir Pavlovich 1 Leonov, Yu. G. 1 Linnell, Peter Arnold 1 Lubotzky, Alexander 1 Lysenok, Igor’ Geront’evich 1 Lyubashenko, Volodymyr V. 1 Machi, Antonio 1 Mal’tsev, Yuriĭ Nikolaevich 1 Mamaghani, M. J. 1 Margulis, Grigoriĭ Aleksandrovich 1 Maslov, Viktor Pavlovich 1 Mazorchuk, Volodymyr 1 Medynets, K. S. 1 Medynets, Kostya 1 Mihalik, Michael L. 1 Mikhalëv, Aleksandr Vasil’evich 1 Mishchenko, Evgeniĭ Frolovich ...and 50 more Co-Authors
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#### Serials

 11 Mathematical Notes 7 Algebra and Discrete Mathematics 4 International Journal of Algebra and Computation 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Proceedings of the Steklov Institute of Mathematics 4 Bulletin of Mathematical Sciences 3 Russian Mathematical Surveys 3 Ukraïns’kyĭ Matematychnyĭ Zhurnal 3 Functional Analysis and its Applications 3 L’Enseignement Mathématique. 2e Série 3 Naukovyĭ Visnyk Chernivets’kogo Universytetu. Matematyka 3 Groups, Geometry, and Dynamics 2 Israel Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Geometriae Dedicata 2 Mathematics of the USSR. Izvestiya 2 Soviet Mathematics. Doklady 2 Transactions of the American Mathematical Society 2 Mathematics of the USSR, Sbornik 2 Sbornik: Mathematics 2 Contemporary Mathematics 2 Journal of Modern Dynamics 1 Matematicheskie Zametki 1 Moscow University Mathematics Bulletin 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Theory of Probability and its Applications 1 Advances in Mathematics 1 Algebra and Logic 1 Algebra i Logika 1 Archiv der Mathematik 1 Commentarii Mathematici Helvetici 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Matematicheskiĭ Sbornik. Novaya Seriya 1 Mathematische Annalen 1 Theoretical Computer Science 1 European Journal of Combinatorics 1 Geometric and Functional Analysis. GAFA 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Bulletin of the American Mathematical Society. New Series 1 Zapiski Nauchnykh Seminarov POMI 1 Journal of Mathematical Sciences (New York) 1 Serdica Mathematical Journal 1 Doklady Mathematics 1 Matematychni Studiï 1 Journal of Dynamical and Control Systems 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 1 Journal of Physics A: Mathematical and Theoretical 1 Involve 1 São Paulo Journal of Mathematical Sciences 1 Groups, Complexity, Cryptology 1 Carpathian Mathematical Publications
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#### Fields

 113 Group theory and generalizations (20-XX) 33 Dynamical systems and ergodic theory (37-XX) 26 Abstract harmonic analysis (43-XX) 18 Computer science (68-XX) 16 Combinatorics (05-XX) 13 Manifolds and cell complexes (57-XX) 12 Probability theory and stochastic processes (60-XX) 9 General and overarching topics; collections (00-XX) 9 Measure and integration (28-XX) 8 Topological groups, Lie groups (22-XX) 7 History and biography (01-XX) 6 Functional analysis (46-XX) 5 Associative rings and algebras (16-XX) 3 Operator theory (47-XX) 2 Number theory (11-XX) 2 Nonassociative rings and algebras (17-XX) 2 Algebraic topology (55-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

114 Publications have been cited 1,727 times in 888 Documents Cited by Year
On Burnside’s problem on periodic groups. Zbl 0595.20029
Grigorchuk, R. I.
1980
Degrees of growth of finitely generated groups, and the theory of invariant means. Zbl 0583.20023
Grigorchuk, R. I.
1985
Automata, dynamical systems, and groups. Zbl 1155.37311
Grigorchuk, R. I.; Nekrashevich, V. V.; Sushchanskii, V. I.
2000
The lamplighter group as a group generated by a 2-state automaton, and its spectrum. Zbl 0990.60049
Grigorchuk, Rostislav I.; Żuk, Andrzej
2001
Just infinite branch groups. Zbl 0982.20024
Grigorchuk, R. I.
2000
Branch groups. Zbl 1140.20306
Bartholdi, Laurent; Grigorchuk, Rostislav I.; Šuniḱ, Zoran
2003
On problems related to growth, entropy, and spectrum in group theory. Zbl 0949.20033
Grigorchuk, R.; de la Harpe, P.
1997
From fractal groups to fractal sets. Zbl 1037.20040
Bartholdi, Laurent; Grigorchuk, Rostislav; Nekrashevych, Volodymyr
2003
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces. Zbl 0968.43002
de la Harpe, P.; Grigorchuk, R. I.; Ceccherini-Silberstein, T.
1999
Solved and unsolved problems around one group. Zbl 1165.20021
Grigorchuk, Rostislav
2005
On Milnor’s problem of group growth. Zbl 0547.20025
Grigorchuk, R. I.
1983
On the spectrum of Hecke type operators related to some fractal groups. Zbl 1172.37305
Bartholdi, L.; Grigorchuk, R. I.
2000
On a torsion-free weakly branch group defined by a three state automaton. Zbl 1070.20031
Grigorchuk, Rostislav I.; Żuk, Andrzej
2002
On a question of Atiyah. Zbl 0969.57022
Grigorchuk, Rostislav I.; Linnell, Peter; Schick, Thomas; Żuk, Andrzej
2000
Some topics in the dynamics of group actions on rooted trees. Zbl 1268.20027
Grigorchuk, R. I.
2011
On parabolic subgroups and Hecke algebras of some fractal groups. Zbl 1011.20028
Bartholdi, Laurent; Grigorchuk, Rotislav I.
2002
Symmetrical random walks on discrete groups. Zbl 0475.60007
Grigorchuk, R. I.
1980
An example of a finitely presented amenable group not belonging to the class $$EG$$. Zbl 0931.43003
Grigorchuk, R. I.
1998
Asymptotic aspects of Schreier graphs and Hanoi Towers groups. Zbl 1135.20016
Grigorchuk, Rostislav; Šuniḱ, Zoran
2006
Some results on bounded cohomology. Zbl 0853.20034
Grigorchuk, R. I.
1995
On growth in group theory. Zbl 0749.20016
Grigorchuk, Rostislav I.
1991
On rates of growth of p-groups and torsion-free groups. Zbl 0568.20033
Grigorchuk, R. I.
1985
The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps. Zbl 1177.05124
Grigorchuk, Rostislav I.; Żuk, Andrzej
2004
Lie methods in growth of groups and groups of finite width. Zbl 1032.20026
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2000
On semigroups with reductions of the degree of growth. Zbl 0643.20036
Grigorchuk, R. I.
1988
On the growth rates of p-groups and torsion-free groups. Zbl 0583.20024
Grigorchuk, R. I.
1986
Milnor’s problem on the growth of groups and its consequences. Zbl 1325.20034
Grigorchuk, Rostislav
2014
Groups of intermediate growth: an introduction. Zbl 1204.20049
Grigorchuk, Rostislav; Pak, Igor
2008
Self-similarity and branching in group theory. Zbl 1185.20044
Grigorchuk, Rostislav; Šunić, Zoran
2007
A structural property concerning abstract commensurability of subgroups. Zbl 1063.20033
Grigorchuk, R. I.; Wilson, J. S.
2003
Schreier spectrum of the Hanoi Towers group on three pegs. Zbl 1170.37008
Grigorchuk, Rostislav; Šunić, Zoran
2008
On the asymptotic spectrum of random walks on infinite families of graphs. Zbl 0957.60044
Grigorchuk, Rostislav I.; Żuk, Andrzej
1999
On quadratic equations in free groups. Zbl 0778.20013
Grigorchuk, R. I.; Kurchanov, P. F.
1992
Branch groups. Zbl 0994.20027
Grigorchuk, R. I.
2000
On algebraic properties of topological full groups. Zbl 1365.37010
Grigorchuk, R. I.; Medynets, K. S.
2014
Invariant random subgroups of lamplighter groups. Zbl 1334.43006
Bowen, Lewis; Grigorchuk, Rostislav; Kravchenko, Rostyslav
2015
Complete growth functions of hyperbolic groups. Zbl 0880.20024
Grigorchuk, Rostislav; Nagnibeda, Tatiana
1997
On the lattice of subgroups of the lamplighter group. Zbl 1317.20032
Grigorchuk, R.; Kravchenko, R.
2014
Amenable actions of nonamenable groups. Zbl 1127.43001
Grigorchuk, R. I.; Nekrashevych, V. Yu.
2005
Growth and amenability of a semigroup and its group of quotients. Zbl 0726.43002
Grigorchuk, R. I.
1990
Limit behaviour of exponential growth rates for finitely generated groups. Zbl 1004.20018
Grigorchuk, Rotislav; de la Harpe, Pierre
2001
Self-similar groups acting essentially freely on the boundary of the binary rooted tree. Zbl 1308.20025
Grigorchuk, Rostislav; Savchuk, Dmytro
2014
Self-similar groups, operator algebras and Schur complement. Zbl 1133.46029
Grigorchuk, Rostislav; Nekrashevych, Volodymyr
2007
On classification of groups generated by 3-state automata over a 2-letter alphabet. Zbl 1164.20004
Bondarenko, Ievgen; Grigorchuk, Rostislav; Kravchenko, Rostislav; Muntyan, Yevgen; Nekrashevych, Volodymyr; Savchuk, Dmytro; Šunić, Zoran
2008
On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata. Zbl 1114.20303
Grigorchuk, R. I.
1999
Spectral properties of a torsion-free weakly branch group defined by a three state automaton. Zbl 1057.60045
Grigorchuk, Rostislav I.; Żuk, Andrzej
2002
Supramenability and the problem of occurrence of free semigroups. Zbl 0626.43003
Grigorchuk, R. I.
1987
Combinatorial group theory and applications to geometry. Transl. from the Russian by P. M. Cohn. 2nd printing of the 1st ed. 1993. Zbl 0997.20500
Collins, D. J.; Grigorchuk, R. I.; Kurchanov, P. F.; Zieschang, H.
1998
The uniqueness of the actions of certain branch groups on rooted trees. Zbl 1052.20023
Grigorchuk, R. I.; Wilson, J. S.
2003
Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order. Zbl 1383.05196
Grigorchuk, Rostislav; Lenz, Daniel; Nagnibeda, Tatiana
2018
Ergodic properties of boundary actions and the Nielsen-Schreier theory. Zbl 1278.37034
Grigorchuk, Rostislav; Kaimanovich, Vadim A.; Nagnibeda, Tatiana
2012
Amenability and growth of one-relator groups. Zbl 0897.20022
Ceccherini-Silberstein, Tullio G.; Grigorchuk, Rostislav I.
1997
On the gap conjecture concerning group growth. Zbl 1323.20035
Grigorchuk, Rostislav
2014
An example of an indexed language of intermediate growth. Zbl 0913.68121
Grigorchuk, R. I.; Machì, A.
1999
Construction of p-groups of intermediate growth that have a continuum of quotient groups. Zbl 0573.20037
Grigorchuk, R. I.
1984
Ergodic theorems for actions of free groups and free semigroups. Zbl 0957.22006
Grigorchuk, R. I.
1999
A description of solutions of quadratic equations in hyperbolic groups. Zbl 0762.20014
Grigorchuk, R. I.; Lysionok, I. G.
1992
Joint spectrum and the infinite dihedral group. Zbl 1462.47003
Grigorchuk, Rostislav; Yang, Rongwei
2017
Universal groups of intermediate growth and their invariant random subgroups. Zbl 1365.20042
Benli, Mustafa Gökhan; Grigorchuk, Rostislav; Nagnibeda, Tatiana
2015
Bounded cohomology of group constructions. Zbl 0873.20039
Grigorchuk, R. I.
1996
On the Hilbert-Poincaré series of graded algebras associated with groups. Zbl 0695.16009
Grigorchuk, R. I.
1990
One-relator groups of exponential growth have uniformly exponential growth. Zbl 0999.20033
Grigorchuk, R. I.; de la Harpe, P.
2001
Amenability and ergodic properties of topological groups: from Bogolyubov onwards. Zbl 1397.43001
Grigorchuk, Rostislav; de la Harpe, Pierre
2017
Cancellative semigroups of power growth. Zbl 0655.20044
Grigorchuk, R. I.
1988
Some questions of group theory related to geometry. Zbl 0781.20023
Grigorchuk, R. I.; Kurchanov, P. F.
1990
A group of intermediate growth acting by homomorphisms on the real line. Zbl 0806.20027
Grigorchuk, R. I.; Maki, A.
1993
Growth functions, rewriting systems, and the Euler characteristic. Zbl 0860.68084
Grigorchuk, R. I.
1995
On a problem of Day on nonelementary amenable groups in the class of finitely presented groups. Zbl 0930.43001
Grigorchuk, R. I.
1996
Groups generated by 3-state automata over a 2-letter alphabet. I. Zbl 1184.20026
Bondarenko, Ievgen; Grigorchuk, Rostislav; Kravchenko, Rostyslav; Muntyan, Yevgen; Nekrashevych, Volodymyr; Savchuk, Dmytro; Šunić, Zoran
2007
On spectra of Koopman, groupoid and quasi-regular representations. Zbl 06991096
Dudko, Artem; Grigorchuk, Rostislav
2017
Certain questions of group theory connected with geometry. Zbl 0748.20021
Grigorchuk, R. I.; Kurchanov, P. F.
1990
On use of iterates of endomorphisms for constructing groups with specific properties. Zbl 0932.20033
Grigorchuk, R. I.; Mamaghani, M. J.
1997
Parabolic subgroups and representations of branch groups. (Sous-groupes paraboliques et représentations de groupes branchés.) Zbl 1011.20027
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2001
Amenable groups without finitely presented amenable covers. Zbl 1352.20025
Benli, Mustafa Gökhan; Grigorchuk, Rostislav; de la Harpe, Pierre
2013
Schreier graphs of Grigorchuk’s group and a subshift associated to a nonprimitive substitution. Zbl 1371.05123
Grigorchuk, Rostislav; Lenz, Daniel; Nagnibeda, Tatiana
2017
Just-infinite $$C^\ast$$-algebras. Zbl 1396.46044
Grigorchuk, Rostislav; Musat, Magdalena; Rørdam, Mikael
2018
From self-similar groups to self-similar sets and spectra. Zbl 1359.37008
Grigorchuk, Rostislav; Nekrashevych, Volodymyr; Šunić, Zoran
2015
Ergodic decomposition of group actions on rooted trees. Zbl 1362.37013
Grigorchuk, Rostislav; Savchuk, Dmytro
2016
The profinite completion of certain torsion $$p$$-groups. Zbl 0964.20018
Grigorchuk, R. I.; Herfort, W. N.; Zalesskii, P. A.
2000
Spectra of non-commutative dynamical systems and graphs related to fractal groups. Zbl 1006.37008
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2000
Diameters, distortion, and eigenvalues. Zbl 1246.05046
Grigorchuk, Rostislav I.; Nowak, Piotr W.
2012
Supramenability and an imbedding problem of free semigroups. Zbl 0616.43002
Grigorchuk, R. I.
1987
A connection between algorithmic problems and entropy characteristics of groups. Zbl 0596.20022
Grigorchuk, R. I.
1985
On the topological and metric types of surfaces regularly covering a closed surface. Zbl 0702.57001
Grigorchuk, R. I.
1990
The conjugacy problem for certain branch groups. Zbl 1001.20031
Grigorchuk, R. I.; Wilson, J. S.
2000
On diagonal actions of branch groups and the corresponding characters. Zbl 06856658
Dudko, Artem; Grigorchuk, Rostislav
2018
Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra. Zbl 1345.05043
Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.
2016
On the width of elements in free groups. Zbl 0749.20005
Grigorchuk, R. I.; Kurchanov, P. F.
1991
Weight functions on groups and an amenability criterion for Beurling algebras. Zbl 0905.43001
Grigorchuk, R. I.
1996
On Tychonoff groups. Zbl 0908.43001
Grigorchuk, R. I.
1998
The spectral problem, substitutions and iterated monodromy. Zbl 1138.20025
Grigorchuk, Rostislav; Savchuk, Dmytro; Šunić, Zoran
2007
On just-infiniteness of locally finite groups and their $$C^*$$-algebras. Zbl 1371.46042
Belyaev, V.; Grigorchuk, R.; Shumyatsky, P.
2017
Classification of epimorphisms of fundamental groups of surfaces onto free groups. Zbl 0810.20032
Grigorchuk, R. I.; Kurchanov, P. F.
1990
An ergodic theorem for the action of a free semigroup. Zbl 1172.37303
Grigorchuk, R. I.
2000
On amenability of semigroups with cancellation. Zbl 1023.43001
Grigorchuk, R. I.; Stepin, A. M.
1998
The group of asynchronous automata and rational homeomorphisms of the Cantor set. Zbl 0988.37014
Grigorchuk, R. I.; Nekrashevich, V. V.
2000
Characteristic random subgroups of geometric groups and free abelian groups of infinite rank. Zbl 1373.20093
Bowen, Lewis; Grigorchuk, Rostislav; Kravchenko, Rostyslav
2017
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups. Zbl 1388.20017
Dudko, Artem; Grigorchuk, Rostislav
2017
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters. Zbl 1297.20025
Grigorchuk, R. I.; Krylyuk, Ya. S.
2012
The rank gradient and the lamplighter group. Zbl 1248.20029
Allums, Derek J.; Grigorchuk, Rostislav I.
2011
Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order. Zbl 1383.05196
Grigorchuk, Rostislav; Lenz, Daniel; Nagnibeda, Tatiana
2018
Just-infinite $$C^\ast$$-algebras. Zbl 1396.46044
Grigorchuk, Rostislav; Musat, Magdalena; Rørdam, Mikael
2018
On diagonal actions of branch groups and the corresponding characters. Zbl 06856658
Dudko, Artem; Grigorchuk, Rostislav
2018
Joint spectrum and the infinite dihedral group. Zbl 1462.47003
Grigorchuk, Rostislav; Yang, Rongwei
2017
Amenability and ergodic properties of topological groups: from Bogolyubov onwards. Zbl 1397.43001
Grigorchuk, Rostislav; de la Harpe, Pierre
2017
On spectra of Koopman, groupoid and quasi-regular representations. Zbl 06991096
Dudko, Artem; Grigorchuk, Rostislav
2017
Schreier graphs of Grigorchuk’s group and a subshift associated to a nonprimitive substitution. Zbl 1371.05123
Grigorchuk, Rostislav; Lenz, Daniel; Nagnibeda, Tatiana
2017
On just-infiniteness of locally finite groups and their $$C^*$$-algebras. Zbl 1371.46042
Belyaev, V.; Grigorchuk, R.; Shumyatsky, P.
2017
Characteristic random subgroups of geometric groups and free abelian groups of infinite rank. Zbl 1373.20093
Bowen, Lewis; Grigorchuk, Rostislav; Kravchenko, Rostyslav
2017
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups. Zbl 1388.20017
Dudko, Artem; Grigorchuk, Rostislav
2017
On just infinite periodic locally soluble groups. Zbl 1423.20036
Grigorchuk, R.; Shumyatsky, P.
2017
Combinatorics of the subshift associated with Grigorchuk’s group. Zbl 1380.37027
Grigorchuk, Rostislav; Lenz, Daniel; Nagnibeda, Tatiana
2017
Ergodic decomposition of group actions on rooted trees. Zbl 1362.37013
Grigorchuk, Rostislav; Savchuk, Dmytro
2016
Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra. Zbl 1345.05043
Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.
2016
Self-similar groups, automatic sequences, and unitriangular representations. Zbl 1394.20018
Grigorchuk, R.; Leonov, Y.; Nekrashevych, V.; Sushchansky, V.
2016
Invariant random subgroups of lamplighter groups. Zbl 1334.43006
Bowen, Lewis; Grigorchuk, Rostislav; Kravchenko, Rostyslav
2015
Universal groups of intermediate growth and their invariant random subgroups. Zbl 1365.20042
Benli, Mustafa Gökhan; Grigorchuk, Rostislav; Nagnibeda, Tatiana
2015
From self-similar groups to self-similar sets and spectra. Zbl 1359.37008
Grigorchuk, Rostislav; Nekrashevych, Volodymyr; Šunić, Zoran
2015
Milnor’s problem on the growth of groups and its consequences. Zbl 1325.20034
Grigorchuk, Rostislav
2014
On algebraic properties of topological full groups. Zbl 1365.37010
Grigorchuk, R. I.; Medynets, K. S.
2014
On the lattice of subgroups of the lamplighter group. Zbl 1317.20032
Grigorchuk, R.; Kravchenko, R.
2014
Self-similar groups acting essentially freely on the boundary of the binary rooted tree. Zbl 1308.20025
Grigorchuk, Rostislav; Savchuk, Dmytro
2014
On the gap conjecture concerning group growth. Zbl 1323.20035
Grigorchuk, Rostislav
2014
Amenable groups without finitely presented amenable covers. Zbl 1352.20025
Benli, Mustafa Gökhan; Grigorchuk, Rostislav; de la Harpe, Pierre
2013
Ergodic properties of boundary actions and the Nielsen-Schreier theory. Zbl 1278.37034
Grigorchuk, Rostislav; Kaimanovich, Vadim A.; Nagnibeda, Tatiana
2012
Diameters, distortion, and eigenvalues. Zbl 1246.05046
Grigorchuk, Rostislav I.; Nowak, Piotr W.
2012
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters. Zbl 1297.20025
Grigorchuk, R. I.; Krylyuk, Ya. S.
2012
Some topics in the dynamics of group actions on rooted trees. Zbl 1268.20027
Grigorchuk, R. I.
2011
The rank gradient and the lamplighter group. Zbl 1248.20029
Allums, Derek J.; Grigorchuk, Rostislav I.
2011
On Dehn functions of infinite presentations of groups. Zbl 1225.20031
Grigorchuk, Rostislav I.; Ivanov, Sergei V.
2009
Groups generated by 3-state automata over a 2-letter alphabet. II. Zbl 1185.20029
Bondarenko, I.; Grigorchuk, R.; Kravchenko, R.; Muntyan, Y.; Nekrashevych, V.; Savchuk, D.; Šunić, Z.
2009
Groups of intermediate growth: an introduction. Zbl 1204.20049
Grigorchuk, Rostislav; Pak, Igor
2008
Schreier spectrum of the Hanoi Towers group on three pegs. Zbl 1170.37008
Grigorchuk, Rostislav; Šunić, Zoran
2008
On classification of groups generated by 3-state automata over a 2-letter alphabet. Zbl 1164.20004
Bondarenko, Ievgen; Grigorchuk, Rostislav; Kravchenko, Rostislav; Muntyan, Yevgen; Nekrashevych, Volodymyr; Savchuk, Dmytro; Šunić, Zoran
2008
Homomorphic images of branch groups, and Serre’s property (FA). Zbl 1139.20021
Delzant, Thomas; Grigorchuk, Rostislav
2008
Self-similarity and branching in group theory. Zbl 1185.20044
Grigorchuk, Rostislav; Šunić, Zoran
2007
Self-similar groups, operator algebras and Schur complement. Zbl 1133.46029
Grigorchuk, Rostislav; Nekrashevych, Volodymyr
2007
Groups generated by 3-state automata over a 2-letter alphabet. I. Zbl 1184.20026
Bondarenko, Ievgen; Grigorchuk, Rostislav; Kravchenko, Rostyslav; Muntyan, Yevgen; Nekrashevych, Volodymyr; Savchuk, Dmytro; Šunić, Zoran
2007
The spectral problem, substitutions and iterated monodromy. Zbl 1138.20025
Grigorchuk, Rostislav; Savchuk, Dmytro; Šunić, Zoran
2007
Asymptotic aspects of Schreier graphs and Hanoi Towers groups. Zbl 1135.20016
Grigorchuk, Rostislav; Šuniḱ, Zoran
2006
Topological and asymptotic aspects of group theory. AMS special session on probabilistic and asymptotic aspects of group theory, Athens, OH, USA, March 26–27, 2004 and the AMS special session on topological aspects of group theory, Nashville, TN, USA, October 16–17, 2004. Zbl 1085.20501
Grigorchuk, Rostislav; Mihalik, Michael; Sapir, Mark; Šuniḱ, Zoran
2006
Solved and unsolved problems around one group. Zbl 1165.20021
Grigorchuk, Rostislav
2005
Amenable actions of nonamenable groups. Zbl 1127.43001
Grigorchuk, R. I.; Nekrashevych, V. Yu.
2005
The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps. Zbl 1177.05124
Grigorchuk, Rostislav I.; Żuk, Andrzej
2004
The group of automorphisms of a 3-generated 2-group of intermediate growth. Zbl 1088.20020
Grigorchuk, R. I.; Sidki, S. N.
2004
A minimality property of certain branch groups. Zbl 1139.20302
Grigorchuk, R. I.; Wilson, J. S.
2004
Branch groups. Zbl 1140.20306
Bartholdi, Laurent; Grigorchuk, Rostislav I.; Šuniḱ, Zoran
2003
From fractal groups to fractal sets. Zbl 1037.20040
Bartholdi, Laurent; Grigorchuk, Rostislav; Nekrashevych, Volodymyr
2003
A structural property concerning abstract commensurability of subgroups. Zbl 1063.20033
Grigorchuk, R. I.; Wilson, J. S.
2003
The uniqueness of the actions of certain branch groups on rooted trees. Zbl 1052.20023
Grigorchuk, R. I.; Wilson, J. S.
2003
On a torsion-free weakly branch group defined by a three state automaton. Zbl 1070.20031
Grigorchuk, Rostislav I.; Żuk, Andrzej
2002
On parabolic subgroups and Hecke algebras of some fractal groups. Zbl 1011.20028
Bartholdi, Laurent; Grigorchuk, Rotislav I.
2002
Spectral properties of a torsion-free weakly branch group defined by a three state automaton. Zbl 1057.60045
Grigorchuk, Rostislav I.; Żuk, Andrzej
2002
The lamplighter group as a group generated by a 2-state automaton, and its spectrum. Zbl 0990.60049
Grigorchuk, Rostislav I.; Żuk, Andrzej
2001
Limit behaviour of exponential growth rates for finitely generated groups. Zbl 1004.20018
Grigorchuk, Rotislav; de la Harpe, Pierre
2001
One-relator groups of exponential growth have uniformly exponential growth. Zbl 0999.20033
Grigorchuk, R. I.; de la Harpe, P.
2001
Parabolic subgroups and representations of branch groups. (Sous-groupes paraboliques et représentations de groupes branchés.) Zbl 1011.20027
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2001
Automata, dynamical systems, and groups. Zbl 1155.37311
Grigorchuk, R. I.; Nekrashevich, V. V.; Sushchanskii, V. I.
2000
Just infinite branch groups. Zbl 0982.20024
Grigorchuk, R. I.
2000
On the spectrum of Hecke type operators related to some fractal groups. Zbl 1172.37305
Bartholdi, L.; Grigorchuk, R. I.
2000
On a question of Atiyah. Zbl 0969.57022
Grigorchuk, Rostislav I.; Linnell, Peter; Schick, Thomas; Żuk, Andrzej
2000
Lie methods in growth of groups and groups of finite width. Zbl 1032.20026
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2000
Branch groups. Zbl 0994.20027
Grigorchuk, R. I.
2000
The profinite completion of certain torsion $$p$$-groups. Zbl 0964.20018
Grigorchuk, R. I.; Herfort, W. N.; Zalesskii, P. A.
2000
Spectra of non-commutative dynamical systems and graphs related to fractal groups. Zbl 1006.37008
Bartholdi, Laurent; Grigorchuk, Rostislav I.
2000
The conjugacy problem for certain branch groups. Zbl 1001.20031
Grigorchuk, R. I.; Wilson, J. S.
2000
An ergodic theorem for the action of a free semigroup. Zbl 1172.37303
Grigorchuk, R. I.
2000
The group of asynchronous automata and rational homeomorphisms of the Cantor set. Zbl 0988.37014
Grigorchuk, R. I.; Nekrashevich, V. V.
2000
Dynamical systems, automata, and infinite groups. Collected papers. (Dinamicheskie sistemy, avtomaty i beskonechnye gruppy. Sbornik statej.) Zbl 0967.00015
Grigorchuk, R. I.
2000
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces. Zbl 0968.43002
de la Harpe, P.; Grigorchuk, R. I.; Ceccherini-Silberstein, T.
1999
On the asymptotic spectrum of random walks on infinite families of graphs. Zbl 0957.60044
Grigorchuk, Rostislav I.; Żuk, Andrzej
1999
On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata. Zbl 1114.20303
Grigorchuk, R. I.
1999
An example of an indexed language of intermediate growth. Zbl 0913.68121
Grigorchuk, R. I.; Machì, A.
1999
Ergodic theorems for actions of free groups and free semigroups. Zbl 0957.22006
Grigorchuk, R. I.
1999
An example of a finitely presented amenable group not belonging to the class $$EG$$. Zbl 0931.43003
Grigorchuk, R. I.
1998
Combinatorial group theory and applications to geometry. Transl. from the Russian by P. M. Cohn. 2nd printing of the 1st ed. 1993. Zbl 0997.20500
Collins, D. J.; Grigorchuk, R. I.; Kurchanov, P. F.; Zieschang, H.
1998
On Tychonoff groups. Zbl 0908.43001
Grigorchuk, R. I.
1998
On amenability of semigroups with cancellation. Zbl 1023.43001
Grigorchuk, R. I.; Stepin, A. M.
1998
On problems related to growth, entropy, and spectrum in group theory. Zbl 0949.20033
Grigorchuk, R.; de la Harpe, P.
1997
Complete growth functions of hyperbolic groups. Zbl 0880.20024
Grigorchuk, Rostislav; Nagnibeda, Tatiana
1997
Amenability and growth of one-relator groups. Zbl 0897.20022
Ceccherini-Silberstein, Tullio G.; Grigorchuk, Rostislav I.
1997
On use of iterates of endomorphisms for constructing groups with specific properties. Zbl 0932.20033
Grigorchuk, R. I.; Mamaghani, M. J.
1997
Bounded cohomology of group constructions. Zbl 0873.20039
Grigorchuk, R. I.
1996
On a problem of Day on nonelementary amenable groups in the class of finitely presented groups. Zbl 0930.43001
Grigorchuk, R. I.
1996
Weight functions on groups and an amenability criterion for Beurling algebras. Zbl 0905.43001
Grigorchuk, R. I.
1996
Some results on bounded cohomology. Zbl 0853.20034
Grigorchuk, R. I.
1995
Growth functions, rewriting systems, and the Euler characteristic. Zbl 0860.68084
Grigorchuk, R. I.
1995
A group of intermediate growth acting by homomorphisms on the real line. Zbl 0806.20027
Grigorchuk, R. I.; Maki, A.
1993
On quadratic equations in free groups. Zbl 0778.20013
Grigorchuk, R. I.; Kurchanov, P. F.
1992
A description of solutions of quadratic equations in hyperbolic groups. Zbl 0762.20014
Grigorchuk, R. I.; Lysionok, I. G.
1992
Equivalence of homomorphisms of surface groups to free groups and some properties of 3-dimensional handlebodies. Zbl 0792.20022
Grigorchuk, R. I.; Kurchanov, P. F.; Zieschang, H.
1992
On growth in group theory. Zbl 0749.20016
Grigorchuk, Rostislav I.
1991
On the width of elements in free groups. Zbl 0749.20005
Grigorchuk, R. I.; Kurchanov, P. F.
1991
Width of elements in free groups. Zbl 0786.20011
Grigorchuk, R. I.; Kurchanov, P. F.
1991
Growth and amenability of a semigroup and its group of quotients. Zbl 0726.43002
Grigorchuk, R. I.
1990
On the Hilbert-Poincaré series of graded algebras associated with groups. Zbl 0695.16009
Grigorchuk, R. I.
1990
Some questions of group theory related to geometry. Zbl 0781.20023
Grigorchuk, R. I.; Kurchanov, P. F.
1990
Certain questions of group theory connected with geometry. Zbl 0748.20021
Grigorchuk, R. I.; Kurchanov, P. F.
1990
On the topological and metric types of surfaces regularly covering a closed surface. Zbl 0702.57001
Grigorchuk, R. I.
1990
Classification of epimorphisms of fundamental groups of surfaces onto free groups. Zbl 0810.20032
Grigorchuk, R. I.; Kurchanov, P. F.
1990
...and 14 more Documents
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#### Cited by 807 Authors

 40 Grigorchuk, Rostislav Ivanovich 23 Bartholdi, Laurent 21 Nekrashevych, Volodymyr V. 20 D’angeli, Daniele 20 Myasnikov, Alexei G. 17 Ceccherini-Silberstein, Tullio G. 14 Erschler, Anna 13 Rodaro, Emanuele 12 Woess, Wolfgang 11 Donno, Alfredo 11 Šunić, Zoran 10 Bondarenko, Ievgen V. 10 Nagnibeda, Tatiana 10 Scarabotti, Fabio 10 Woryna, Adam 9 Kharlampovich, Olga G. 9 Osin, Denis V. 9 Petrogradsky, Victor Mikhaylovich 9 Savchuk, Dmytro M. 8 Glasner, Yair 8 Sushchans’kyĭ, Vitaliĭ Ivanovych 7 Brieussel, Jérémie 7 Klimann, Ines 6 Abért, Miklós 6 Bowen, Lewis Phylip 6 de la Harpe, Pierre 6 Elder, Murray J. 6 Fernández-Alcober, Gustavo A. 6 Garrido, Alejandra 6 Guba, Victor S. 6 Monod, Nicolas 6 Ol’shanskiĭ, Aleksandr Yur’evich 6 Pak, Igor 6 Sambusetti, Andrea 6 Sapir, Mark Valentinovich 6 Steinberg, Benjamin 6 Thomas, Simon R. 6 Tolli, Filippo 6 Virág, Bálint 6 Wächter, Jan Philipp 5 Arzhantseva, Goulnara N. 5 Cain, Alan J. 5 Cavaleri, Matteo 5 Dudko, Artem 5 Kaimanovich, Vadim A. 5 Kechris, Alexander S. 5 Leonov, Yu. G. 5 Machi, Antonio 5 Noce, Marialaura 5 Nowak, Piotr W. 5 Shalev, Aner 5 Shestakov, Ivan Pavlovich 5 Skipper, Rachel 5 Vorobets, Yaroslav 5 Yang, Rongwei 4 Ara, Pere 4 Benli, Mustafa Gökhan 4 Bleak, Collin 4 Burillo, José 4 Cashen, Christopher H. 4 de Cornulier, Yves 4 Elek, Gábor 4 Francoeur, Dominik 4 Hartung, René 4 Jespers, Eric 4 Kagan, Dmitrii Z. 4 Kapovich, Ilya 4 Kravchenko, Rostyslav V. 4 Lawson, Mark Verus 4 Lenz, Daniel H. 4 Lubotzky, Alexander 4 Lysenok, Igor’ Geront’evich 4 Matte Bon, Nicolás 4 Okniński, Jan 4 Picantin, Matthieu 4 Pittet, Christophe 4 Rozhkov, A. V. 4 Samet-Vaillant, Aryeh Y. 4 Seifter, Norbert 4 Shneerson, L. M. 4 Shumyatsky, Pavel 4 Silva, Pedro V. 4 Steinhurst, Benjamin 4 Uria-Albizuri, Jone 4 Wesolek, Phillip Richard 4 Wilson, John Stuart 4 Zel’manov, Efim Isaakovich 4 Żuk, Andrzej 3 Akhmedov, Azer 3 Barnea, Yiftach 3 Belk, James M. 3 Biringer, Ian 3 Bou-Rabee, Khalid 3 Bridson, Martin R. 3 Brunner, Andrew Michael 3 Bufetov, Aleksandr Igorevich 3 Caprace, Pierre-Emmanuel 3 Ciobanu, Laura 3 Damanik, David 3 Dobrynina, Irina Vasil’evna ...and 707 more Authors
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#### Cited in 187 Serials

 84 Journal of Algebra 56 International Journal of Algebra and Computation 45 Groups, Geometry, and Dynamics 33 Transactions of the American Mathematical Society 28 Geometriae Dedicata 24 Proceedings of the American Mathematical Society 23 Israel Journal of Mathematics 23 Journal of Mathematical Sciences (New York) 19 Mathematical Notes 18 Journal of Functional Analysis 18 Theoretical Computer Science 17 Advances in Mathematics 15 Annales de l’Institut Fourier 14 Mathematische Annalen 14 European Journal of Combinatorics 13 Ergodic Theory and Dynamical Systems 12 Inventiones Mathematicae 12 Journal of Group Theory 10 Communications in Algebra 10 Semigroup Forum 10 Proceedings of the Steklov Institute of Mathematics 9 Duke Mathematical Journal 9 Journal of Pure and Applied Algebra 8 Archiv der Mathematik 8 Topology and its Applications 8 Expositiones Mathematicae 7 Communications in Mathematical Physics 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 The Annals of Probability 7 Bulletin of Mathematical Sciences 6 Journal of the London Mathematical Society. Second Series 6 Monatshefte für Mathematik 6 Geometric and Functional Analysis. GAFA 6 Journal of the European Mathematical Society (JEMS) 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Modern Dynamics 5 Journal d’Analyse Mathématique 5 Algebra and Logic 5 Bulletin of the London Mathematical Society 5 Compositio Mathematica 5 Journal of Combinatorial Theory. Series B 5 Mathematische Zeitschrift 5 Journal of Algebra and its Applications 4 Discrete Mathematics 4 Journal of Mathematical Analysis and Applications 4 Memoirs of the American Mathematical Society 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Probability Theory and Related Fields 4 Linear Algebra and its Applications 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Annals of Mathematics. Second Series 4 Journal of Topology and Analysis 4 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 4 International Journal of Group Theory 3 Discrete Applied Mathematics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Functional Analysis and its Applications 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Annals of Pure and Applied Logic 3 Journal of the American Mathematical Society 3 The Journal of Geometric Analysis 3 Russian Journal of Mathematical Physics 3 The Electronic Journal of Combinatorics 3 Geometry & Topology 3 Algebra and Discrete Mathematics 2 Rocky Mountain Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Journal of Geometry and Physics 2 Illinois Journal of Mathematics 2 Journal of Computer and System Sciences 2 Rendiconti del Seminario Matematico della Università di Padova 2 Results in Mathematics 2 Advances in Applied Mathematics 2 Revista Matemática Iberoamericana 2 Information and Computation 2 Forum Mathematicum 2 Experimental Mathematics 2 Topology Proceedings 2 Journal de Théorie des Nombres de Bordeaux 2 St. Petersburg Mathematical Journal 2 Annales Mathématiques Blaise Pascal 2 Fractals 2 Electronic Research Announcements of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Theory of Computing Systems 2 Conformal Geometry and Dynamics 2 LMS Journal of Computation and Mathematics 2 Acta Mathematica Sinica. English Series 2 Journal of Dynamical and Control Systems 2 Lobachevskii Journal of Mathematics 2 Algebraic & Geometric Topology 2 Journal of the Australian Mathematical Society 2 Groups, Complexity, Cryptology 2 Carpathian Mathematical Publications 2 Discrete Analysis 2 Journal of Combinatorial Algebra 1 Bulletin of the Australian Mathematical Society 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics ...and 87 more Serials
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#### Cited in 47 Fields

 598 Group theory and generalizations (20-XX) 164 Combinatorics (05-XX) 155 Dynamical systems and ergodic theory (37-XX) 115 Computer science (68-XX) 99 Abstract harmonic analysis (43-XX) 98 Topological groups, Lie groups (22-XX) 80 Probability theory and stochastic processes (60-XX) 74 Manifolds and cell complexes (57-XX) 59 Functional analysis (46-XX) 50 Associative rings and algebras (16-XX) 36 Measure and integration (28-XX) 35 Mathematical logic and foundations (03-XX) 33 Operator theory (47-XX) 31 Differential geometry (53-XX) 30 Number theory (11-XX) 26 Nonassociative rings and algebras (17-XX) 20 General topology (54-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Algebraic geometry (14-XX) 11 Quantum theory (81-XX) 10 Functions of a complex variable (30-XX) 10 Algebraic topology (55-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Category theory; homological algebra (18-XX) 8 Partial differential equations (35-XX) 6 Potential theory (31-XX) 6 Difference and functional equations (39-XX) 6 Convex and discrete geometry (52-XX) 6 Information and communication theory, circuits (94-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Commutative algebra (13-XX) 5 Operations research, mathematical programming (90-XX) 4 Mechanics of particles and systems (70-XX) 3 Real functions (26-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Ordinary differential equations (34-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 $$K$$-theory (19-XX) 2 Relativity and gravitational theory (83-XX) 1 General algebraic systems (08-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Optics, electromagnetic theory (78-XX)

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