## $$p$$-Adic Numbers, Ultrametric Analysis, and Applications

 Short Title: $$p$$-Adic Numbers Ultrametric Anal. Appl. Publisher: Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK “Nauka/Interperiodica”, Moscow ISSN: 2070-0466; 2070-0474/e Online: http://link.springer.com/journal/volumesAndIssues/12607 Comments: Indexed cover-to-cover
 Documents Indexed: 357 Publications (since 2009) References Indexed: 353 Publications with 8,264 References.
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### Latest Issues

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### Authors

 25 Khrennikov, Andreĭ Yur’evich 19 Kozyrev, Sergeĭ Vladimirovich 13 Volovich, Igor’ Vasil’evich 12 Escassut, Alain 12 Volosivets, Sergeĭ Sergeevich 11 Dragovich, Branko 9 Albeverio, Sergio A. 9 Dovgoshey, Oleksiy Alfredovich 7 Petrov, Evgenii Aleksandrovich 6 Diarra, Bertin 6 Iurato, Giuseppe 6 Marcolli, Matilde 6 Nguyen Minh Chuong 6 Platonov, Sergei S. 5 Bradley, Patrick Erik 5 Duong, Dao Van 5 Kaneko, Hiroshi 5 Memić, Nacima 5 Murtagh, Fionn D. 5 Shamseddine, Khodr 5 Zubarev, Aleksandr Petrovich 5 Zúñiga-Galindo, Wilson A. 4 Bikulov, Al’bert Khakimovich 4 Casas-Sánchez, Oscar Francisco 4 Digernes, Trond 4 Khachatryan, Khachatur Aghavardovich 4 Mukhamedov, Farruh Maksutovich 4 Natarajan, Pinnangudi Narayanasubramanian 4 Rozikov, Utkir A. 4 Sattarov, Iskandar A. 4 Vladimirov, Vasiliĭ Sergeevich 3 Aguayo, José N. 3 Anashin, Vladimir Sergeevich 3 Bottazzi, Emanuele 3 Boussaf, Kamal 3 Chacón-Cortes, Leonardo Fabio 3 Chatyrko, Vitalij A. 3 Estala-Arias, Samuel 3 Galeano-Peñaloza, Jeanneth 3 Khakimov, Otabek N. 3 Kochubeĭ, Anatoliĭ Naumovych 3 Matsumoto, Hisaaki 3 Missarov, Mukadas D. 3 Mounkoro, Tongobè 3 Nova, Miguel 3 Ojeda, Jacqueline 3 Sakbaev, Vsevolod Zhanovich 3 Shelkovich, Vladimir M. 3 Trojovský, Pavel 3 Trushechkin, Anton Sergeevich 3 Varadarajan, Veeravalli S. 3 Yasuda, Kumi 3 Zelenov, Evgenii I. 2 Accardi, Luigi 2 Aguilar-Arteaga, Victor A. 2 An, Vu Hoai An 2 Aref’eva, Irina Yaroslavna 2 Blanco-Chacón, Iván 2 Cruz-López, Manuel 2 Diagana, Toka 2 Doğan, Mutlay 2 Dung, Kieu Huu 2 Dupré, Nicolas 2 Farkov, Yuriĭ Anatol’evich 2 Fioresi, Rita 2 Glöckner, Helge 2 Hùng, Lũ’ 2 Hussain, Amjad 2 Iijima, Ryota 2 Katanaev, Mikhaĭl Orinovich 2 Khachatryan, Aghavard Khachaturovich 2 Kozlov, Valeriĭ Vasil’evich 2 Lapidus, Michel L. 2 Lelis, Jean 2 Lindahl, Karl-Olof 2 Maïga, Hamadoun 2 Mamghaderi, Hamid 2 Manin, Yuri Ivanovich 2 Marques, Diego 2 Marrani, Alessio 2 Masiha, Hashem Parvaneh 2 Matevosyan, Hovik A. 2 Nagel, Enno 2 Ohya, Masanori 2 Olivos, Elena 2 Pechen, Alexander Nikolaevich 2 Qiu, Derong 2 Rakić, Zoran 2 Rodríguez Vega, John Jaime 2 Sarfraz, Naqash 2 Schmidt, Rene 2 Skopina, Maria A. 2 Sopin, Valeriĭ V. 2 Sylla, Djeidi 2 Tangara, Fana 2 Tukhtabaev, Akbarkhuja 2 van der Walt, Jan Harm 1 Abdesselam, Abdelmalek 1 Ackerman, Nathanael Leedom 1 Alharbi, Nof ...and 223 more Authors
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### Fields

 105 Number theory (11-XX) 64 Functional analysis (46-XX) 56 Quantum theory (81-XX) 41 Operator theory (47-XX) 39 Dynamical systems and ergodic theory (37-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 33 Probability theory and stochastic processes (60-XX) 29 Real functions (26-XX) 27 Field theory and polynomials (12-XX) 27 General topology (54-XX) 26 Functions of a complex variable (30-XX) 26 Partial differential equations (35-XX) 24 Statistical mechanics, structure of matter (82-XX) 21 Combinatorics (05-XX) 13 Computer science (68-XX) 12 Measure and integration (28-XX) 11 Algebraic geometry (14-XX) 11 Relativity and gravitational theory (83-XX) 11 Biology and other natural sciences (92-XX) 9 Nonassociative rings and algebras (17-XX) 9 Abstract harmonic analysis (43-XX) 9 Differential geometry (53-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 History and biography (01-XX) 8 Numerical analysis (65-XX) 7 Topological groups, Lie groups (22-XX) 7 Sequences, series, summability (40-XX) 7 Information and communication theory, circuits (94-XX) 6 Group theory and generalizations (20-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Statistics (62-XX) 5 Mathematical logic and foundations (03-XX) 5 Mechanics of particles and systems (70-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Associative rings and algebras (16-XX) 3 Potential theory (31-XX) 3 Ordinary differential equations (34-XX) 3 Integral equations (45-XX) 3 Manifolds and cell complexes (57-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Approximations and expansions (41-XX) 2 Fluid mechanics (76-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX)

### Citations contained in zbMATH Open

231 Publications have been cited 1,320 times in 703 Documents Cited by Year
On $$p$$-adic mathematical physics. Zbl 1187.81004
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V.
2009
Number theory as the ultimate physical theory. Zbl 1258.81074
Volovich, Igor V.
2010
A $$p$$-adic model of DNA sequence and genetic code. Zbl 1187.92039
Dragovich, B.; Dragovich, A. Yu.
2009
$$p$$-adic mathematical physics: the first 30 years. Zbl 1394.81009
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V.; Zelenov, E. I.
2017
Using grossone to count the number of elements of infinite sets and the connection with bijections. Zbl 1259.03064
Margenstern, Maurice
2011
van der Put basis and $$p$$-adic dynamics. Zbl 1250.37037
Yurova, Ekaterina
2010
$$p$$-adic orthogonal wavelet bases. Zbl 1187.42033
Khrennikov, A. Yu.; Shelkovich, V. M.; Skopina, M.
2009
Multidimensional Hausdorff operator on $$p$$-adic field. Zbl 1287.47059
Volosivets, S. S.
2010
Multidimensional basis of $$p$$-adic wavelets and representation theory. Zbl 1187.42030
Albeverio, Sergio; Kozyrev, Sergei V.
2009
$$p$$-adic valued quantization. Zbl 1187.81137
Albeverio, Sergio; Cianci, Roberto; Khrennikov, Andrei Yu.
2009
On $$p$$-adic quasi Gibbs measures for $$q+1$$-state Potts model on the Cayley tree. Zbl 1268.82007
Mukhamedov, Farrukh
2010
Diameter and diametrical pairs of points in ultrametric spaces. Zbl 1304.54049
Dordovskyi, Dmitry; Dovgoshey, Oleksiy; Petrov, Eugeniy
2011
Weighted Hardy-Littlewood operators and commutators on $$p$$-adic functional spaces. Zbl 1271.42029
Chuong, N. M.; Duong, D. V.
2013
Digraph representations of rational functions over the $$p$$-adic numbers. Zbl 1259.37065
Diao, Hansheng; Silva, Cesar E.
2011
On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function. Zbl 1268.11114
Sergeyev, Yaroslav D.
2011
Hausdorff operator of special kind in Morrey and Herz $$p$$-adic spaces. Zbl 1271.42038
Volosivets, S. S.
2012
Functional classical mechanics and rational numbers. Zbl 1387.70003
Trushechkin, Anton S.; Volovich, Igor V.
2009
Ultrametricity and metric betweenness in tangent spaces to metric spaces. Zbl 1276.53052
Dovgoshey, Oleksiy; Dordovskyi, Dmytro
2010
Algorithms for wavelet construction on Vilenkin groups. Zbl 1254.42044
Farkov, Yuri A.; Rodionov, Evgeny A.
2011
The $$p$$-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space. Zbl 1369.47080
Chuong, N. M.; Duong, D. V.
2016
Frames of $$p$$-adic wavelets and orbits of the affine group. Zbl 1187.42029
Albeverio, S.; Kozyrev, S. V.
2009
An infinite family of $$p$$-adic non-Haar wavelet bases and pseudo-differential operators. Zbl 1187.42034
Khrennikov, Andrei Yu.; Shelkovich, Vladimir M.
2009
Cyclotomy and endomotives. Zbl 1236.46067
Marcolli, Matilde
2009
Geometry of non-Archimedean Gromov-Hausdorff distance. Zbl 1253.53041
Qiu, Derong
2009
Automata finiteness criterion in terms of van der Put series of automata functions. Zbl 1262.11045
Anashin, V.
2012
On the equations for $$p$$ -adic closed and open strings. Zbl 1187.35305
2009
$$p$$-adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes. Zbl 1317.35309
Casas-Sánchez, O. F.; Zúñiga-Galindo, W. A.
2014
Dynamics on rugged landscapes of energy and ultrametric diffusion. Zbl 1253.82040
Kozyrev, Sergei V.
2010
Quincunx multiresolution analysis for $$L^2(\mathbb Q^2_2)$$. Zbl 1273.42036
King, Emily J.; Skopina, Maria A.
2010
On spaces extremal for the Gomory-Hu inequality. Zbl 1343.05072
Dovgoshey, O.; Petrov, E.; Teichert, H.-M.
2015
On a nonlinear $$p$$-adic dynamical system. Zbl 1347.37148
Rozikov, U. A.; Sattarov, I. A.
2014
On measure-preserving functions over $$\mathbb Z_3$$. Zbl 1291.37122
Yurova, Ekaterina
2012
Some pathways in non-linear supersymmetry: special geometry Born-Infeld’s, cosmology and dualities. Zbl 1337.81069
Ferrara, Sergio; Sagnotti, A.
2015
Twisted spectral triples and quantum statistical mechanical systems. Zbl 1315.58006
Greenfield, M.; Marcolli, M.; Teh, K.
2014
Weak and strong estimates for rough Hausdorff type operator defined on $$p$$-adic linear space. Zbl 06847852
Volosivets, S. S.
2017
On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains. Zbl 1375.31010
Matevossian, Hovik A.
2017
The Hausdorff operator on weighted $$p$$-adic Morrey and Herz type spaces. Zbl 1478.42022
Hussain, Amjad; Sarfraz, Naqash
2019
Some aspects of $$m$$-adic analysis and its applications to $$m$$-adic stochastic processes. Zbl 1268.60076
Dolgopolov, Mikhail V.; Zubarev, Alexander P.
2011
Completeness in generalized ultrametric spaces. Zbl 1320.54017
Ackerman, N. L.
2013
On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains. Zbl 1325.35032
Matevossian, H. A.
2015
Trees and ultrametric Möbius structures. Zbl 1387.53022
Beyrer, Jonas; Schroeder, Victor
2017
Non-Archimedean pseudodifferential operators and Feller semigroups. Zbl 1461.35259
Torresblanca-Badillo, Anselmo; Zúñiga-Galindo, W. A.
2018
From isomorphic rooted trees to isometric ultrametric spaces. Zbl 1435.54011
Dovgoshey, Oleksiy; Petrov, Evgeniy
2018
On $$p$$-adic classification. Zbl 1250.68221
2009
Modelling of psychological behavior on the basis of ultrametric mental space: encoding of categories by balls. Zbl 1260.91221
Khrennikov, Andrei Yu.
2010
Multipliers for the symmetry groups of $$p$$-adic spacetime. Zbl 1187.81141
2009
Cognitive processes of the brain: an ultrametric model of information dynamics in unconsciousness. Zbl 1354.91125
Khrennikov, A. Yu.
2014
The comb representation of compact ultrametric spaces. Zbl 1379.54023
Lambert, Amaury; Uribe Bravo, Gerónimo
2017
Weak similarities of finite ultrametric and semimetric spaces. Zbl 1403.54019
Petrov, Evgeniy
2018
Multidimensional $$p$$-adic wavelets for the deformed metric. Zbl 1257.42045
Albeverio, Sergio; Kozyrev, Sergei V.
2010
Hysteresis model of unconscious-conscious interconnection: exploring dynamics on $$m$$-adic trees. Zbl 1336.91061
Iurato, Giuseppe; Khrennikov, Andrei
2015
The structures of Hausdorff metric in non-Archimedean spaces. Zbl 1318.54015
Qiu, Derong
2014
$$p$$-adic (3, 2)-rational dynamical systems. Zbl 1347.37149
Sattarov, I. A.
2015
Order, type and cotype of growth for $$p$$-adic entire functions: a survey with additional properties. Zbl 1432.30031
Boussaf, Kamal; Boutabaa, Abdelbaki; Escassut, Alain
2016
On $$p$$-adic Gibbs measures for Ising model with four competing interactions. Zbl 1285.82013
Khakimov, O. N.
2013
Finite ultrametric balls. Zbl 1432.54027
Dovgoshey, Oleksiy
2019
Hausdorff operator of special kind on $$p$$-adic field and $$BMO$$-type spaces. Zbl 1254.42011
Volosivets, S. S.
2011
Local zeta functions and fundamental solutions for pseudo-differential operators over $$p$$-adic fields. Zbl 1268.11153
Zúñiga-Galindo, W. A.
2011
$$p$$-adic renormalization group solutions and the Euclidean renormalization group conjectures. Zbl 1251.81047
Missarov, M. D.
2012
On periodic Gibbs measures of $$p$$-adic Potts model on a Cayley tree. Zbl 1356.82022
Mukhamedov, F.; Khakimov, O.
2016
On spaces of $$p$$-adic vector measures. Zbl 1188.46029
Katsaras, A. K.
2009
Self-similar $$p$$-adic fractal strings and their complex dimensions. Zbl 1187.28014
Lapidus, Michel L.; Hùng, Lũ’
2009
Invariant ultrametrics and Markov processes on the finite adèle ring of $$\mathbb{Q}$$. Zbl 1370.11127
Cruz-López, Manuel; Estala-Arias, Samuel
2016
Recurrence equations over trees in a non-Archimedean context. Zbl 1420.47027
Mukhamedov, F.
2014
Formal foundations for the origins of human consciousness. Zbl 1407.91210
Iurato, Giuseppe; Khrennikov, Andrei; Murtagh, F.
2016
An analogue of the Titchmarsh theorem for the Fourier transform on the group of $$p$$-adic numbers. Zbl 1409.11116
Platonov, Sergey S.
2017
On ergodicity of $$p$$-adic dynamical systems for arbitrary prime $$p$$. Zbl 1302.37063
Yurova, E.
2013
Properties and morphisms of finite ultrametric spaces and their representing trees. Zbl 1433.54015
Dovgoshey, Oleksiy; Petrov, Evgeniy
2019
Optimal weak type estimates for $$p$$-adic Hardy operators. Zbl 1434.42034
Hussain, Amjad; Sarfraz, Naqash
2020
On solution properties of some types of $$p$$-adic kinetic equations of the form reaction-diffusion. Zbl 1268.35076
Bikulov, Albert Kh.
2010
Periodic wavelets on the $$p$$-adic Vilenkin group. Zbl 1256.42049
Farkov, Yuri A.
2011
On the variational description of the trajectories of averaging quantum dynamical maps. Zbl 1251.81060
Sakbaev, V. Zh.
2012
The $$p$$-adic analytic subgroup theorem revisited. Zbl 1327.11049
Fuchs, C.; Pham, D. H.
2015
From data to the $$p$$-adic or ultrametric model. Zbl 1187.62111
Murtagh, F.
2009
Quantum approximation theorem. Zbl 1187.81142
Zelenov, E. I.
2009
Wavelet bases in the Lebesgue spaces on the field of $$p$$-adic numbers. Zbl 1322.46014
Chuong, N. M.; Duong, D. V.
2013
On stochastic generation of ultrametrics in high-dimensional Euclidean spaces. Zbl 1315.60020
Zubarev, A. P.
2014
On a generalized $$p$$-adic Gibbs measure for Ising model on trees. Zbl 1311.82011
Khakimov, O. N.
2014
Bounds of $$p$$-adic weighted Hardy-Cesàro operators and their commutators on $$p$$-adic weighted spaces of Morrey types. Zbl 1371.42015
Nguyen Minh Chuong; Ha Duy Hung; Nguyen Thi Hong
2016
An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups. Zbl 1388.43004
Platonov, Sergey S.
2017
Self-adjoint approximations of the degenerate Schrödinger operator. Zbl 06725606
Sakbaev, V. Zh.; Volovich, I. V.
2017
Maximal function and Riesz potential on $$p$$-adic linear spaces. Zbl 1284.42044
Volosivets, S. S.
2013
Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey. Zbl 1428.46047
Bendikov, Alexander
2018
Measure-preservation and the existence of a root of $$p$$-adic 1-Lipschitz functions in Mahler’s expansion. Zbl 1425.26022
Jeong, Sangtae
2018
Active beam splitting attack applied to differential phase shift quantum key distribution protocol. Zbl 1420.81008
Avanesov, A. S.; Kronberg, D. A.; Pechen, A. N.
2018
Hausdorff operator on weighted Lebesgue and grand Lebesgue $$p$$-adic spaces. Zbl 07146202
Bandaliyev, R. A.; Volosivets, S. S.
2019
Graphs, spectral triples and Dirac zeta functions. Zbl 1252.05084
de Jong, Jan Willem
2009
Pseudodifferential $$p$$-adic vector fields and pseudodifferentiation of a composite $$p$$-adic function. Zbl 1288.47048
Albeverio, Sergio; Kozyrev, Sergei V.
2010
Classification of three-dimensional solvable $$p$$-adic Leibniz algebras. Zbl 1305.17002
Khudoyberdiyev, A. Kh.; Kurbanbaev, T. K.; Omirov, B. A.
2010
A Muckenhoupt’s weight problem and vector valued maximal inequalities over local fields. Zbl 1254.42020
Chuong, Nguyen Minh; Hung, Ha Duy
2010
Fast, linear time, $$m$$-adic hierarchical clustering for search and retrieval using the Baire metric, with linkages to generalized ultrametrics, hashing, formal concept analysis, and precision of data measurement. Zbl 06105098
Murtagh, F.; Contreras, P.
2012
Application of $$p$$-adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into $$\mathbb{Q}_p$$. Zbl 1323.60098
Bikulov, A. Kh.; Zubarev, A. P.
2015
Mumford dendrograms and discrete $$p$$-adic symmetries. Zbl 1264.14034
2009
$$p$$-adic invariant summation of some $$p$$-adic functional series. Zbl 1329.40006
Dragovich, B.; Misic, N. Z.
2014
Functional stochastic classical mechanics. Zbl 1367.70002
Volovich, I. V.
2015
Local zeta functions, pseudodifferential operators and Sobolev-type spaces over non-Archimedean local fields. Zbl 1427.11135
Zúñiga-Galindo, W. A.
2017
Generalized fractional integrals in $$p$$-adic Morrey and Herz spaces. Zbl 1410.46058
Volosivets, S. S.
2017
Riesz kernels and pseudodifferential operators attached to quadratic forms over $$p$$-adic fields. Zbl 1301.47104
Casas-Sánchez, O.; Zúñiga-Galindo, W. A.
2013
On integrable delta functions on the Levi-Civita field. Zbl 1428.46048
Flynn, Darren; Shamseddine, Khodr
2018
Towards three-dimensional conformal probability. Zbl 1420.81023
Abdesselam, Abdelmalek
2018
An embedding, an extension, and an interpolation of ultrametrics. Zbl 1481.54025
Ishiki, Yoshito
2021
An incompatibility result on non-Archimedean integration. Zbl 1486.26063
Bottazzi, Emanuele
2021
log-Coulomb gas with norm-density in $$p$$-fields. Zbl 1484.81102
Webster, Joe
2021
A Beilinson-Bernstein theorem for analytic quantum groups. I. Zbl 07449599
Dupré, Nicolas
2021
A Beilinson-Bernstein theorem for analytic quantum groups. II. Zbl 07449600
Dupré, Nicolas
2021
Ultrametric preserving functions and weak similarities of ultrametric spaces. Zbl 1485.54037
Bilet, Viktoriia; Dovgoshey, Oleksiy; Shanin, Ruslan
2021
On quasisymmetric mappings between ultrametric spaces. Zbl 1485.54032
Petrov, Evgeniy; Salimov, Ruslan
2021
Optimal weak type estimates for $$p$$-adic Hardy operators. Zbl 1434.42034
Hussain, Amjad; Sarfraz, Naqash
2020
On some extremal properties of finite ultrametric spaces. Zbl 1473.54027
Dovgoshey, Oleksiy; Petrov, Evgeniy
2020
Counting fixed points and rooted closed walks of the singular map $$x \mapsto x^{x^n}$$ modulo powers of a prime. Zbl 1472.11292
Holden, Joshua; Richardson, Pamela A.; Robinson, Margaret M.
2020
Ergodic uniformly differentiable functions modulo $$p$$ on $$\mathbb{Z}_p$$. Zbl 1435.37015
Memić, Nacima; Huremović, Jasmina Muminović
2020
A survey and new results on Banach algebras of ultrametric continuous functions. Zbl 1468.46079
Chicourrat, Monique; Diarra, Bertin; Escassut, Alain
2020
Embedding theorems for Hölder classes defined on $$p$$-adic linear spaces. Zbl 1434.42037
Volosivets, S. S.
2020
Generalised diffusion on moduli spaces of $$p$$-adic Mumford curves. Zbl 1457.35097
2020
Variable exponent Lebesgue spaces and Hardy-Littlewood maximal function on $$p$$-adic numbers. Zbl 1451.42025
Chacón-Cortés, Leonardo Fabio; Rafeiro, Humberto
2020
Learning problem for functional programming and model of biological evolution. Zbl 1447.92288
Kozyrev, Sergei V.
2020
On the $$\mathbb{K}$$-vector sequential topology on a non-Archimedean valued field. Zbl 1468.46080
El Amrani, Abdelkhalek; Razouki, Abdelhak; Hassani, Rachid A.; Babahmed, Mohamed
2020
Weighted integrability of $$p$$-adic Fourier transform. Zbl 1456.30081
Golubov, Boris I.; Volosivets, Sergey S.
2020
Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups. Zbl 1465.43003
Platonov, Sergey S.
2020
URS and bi-URS for meromorphic functions in a non-Archimedean field. Zbl 1456.30082
Khoai, H. H.; An, V. H.
2020
Notes on ergodic $$2$$-adic transformations. Zbl 1458.37111
Memić, Nacima
2020
The Hausdorff operator on weighted $$p$$-adic Morrey and Herz type spaces. Zbl 1478.42022
Hussain, Amjad; Sarfraz, Naqash
2019
Finite ultrametric balls. Zbl 1432.54027
Dovgoshey, Oleksiy
2019
Properties and morphisms of finite ultrametric spaces and their representing trees. Zbl 1433.54015
Dovgoshey, Oleksiy; Petrov, Evgeniy
2019
Hausdorff operator on weighted Lebesgue and grand Lebesgue $$p$$-adic spaces. Zbl 07146202
Bandaliyev, R. A.; Volosivets, S. S.
2019
Fourier transform of Dini-Lipschitz functions on the field of $$p$$-adic numbers. Zbl 1440.43009
Platonov, Sergey S.
2019
Pseudodifferential operators and Markov processes on adèles. Zbl 1435.35424
Aguilar-Arteaga, Victor A.; Estala-Arias, Samuel
2019
Some problems in the theory of approximation of functions on locally compact Vilenkin groups. Zbl 1430.43002
Platonov, Sergey S.
2019
$$p$$-adic dynamical systems of the function $$\frac{ax}{x^2+a}$$. Zbl 1441.37105
Rozikov, U. A.; Sattarov, I. A.; Yam, S.
2019
Complete integrability of quantum and classical dynamical systems. Zbl 1436.81036
Volovich, Igor V.
2019
Generalized open mapping theorem for $$X$$-normed spaces. Zbl 1443.46047
Comicheo, Angel Barria
2019
$$p$$-adic multiwavelet sets. Zbl 1434.42049
Haldar, Debasis; Singh, Divya
2019
Adinkras, dessins, origami, and supersymmetry spectral triples. Zbl 1445.17002
Marcolli, Matilde; Zolman, Nick
2019
Non periodic $$p$$-adic generalized Gibbs measure for Ising model. Zbl 1437.82009
Rahmatullaev, Muzaffar; Tukhtabaev, Akbarkhuja
2019
Weighted estimates for maximal operators, Riesz potential operators and commutators on $$p$$-adic Lebesgue and Morrey spaces. Zbl 1451.42026
Chuong, Nguyen Minh; Duong, Dao Van; Dung, Kieu Huu
2019
Noncommutative geometry of groups like $$\Gamma_0(N)$$. Zbl 1475.11099
Plazas, Jorge
2019
Non-Archimedean pseudodifferential operators and Feller semigroups. Zbl 1461.35259
Torresblanca-Badillo, Anselmo; Zúñiga-Galindo, W. A.
2018
From isomorphic rooted trees to isometric ultrametric spaces. Zbl 1435.54011
Dovgoshey, Oleksiy; Petrov, Evgeniy
2018
Weak similarities of finite ultrametric and semimetric spaces. Zbl 1403.54019
Petrov, Evgeniy
2018
Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey. Zbl 1428.46047
Bendikov, Alexander
2018
Measure-preservation and the existence of a root of $$p$$-adic 1-Lipschitz functions in Mahler’s expansion. Zbl 1425.26022
Jeong, Sangtae
2018
Active beam splitting attack applied to differential phase shift quantum key distribution protocol. Zbl 1420.81008
Avanesov, A. S.; Kronberg, D. A.; Pechen, A. N.
2018
On integrable delta functions on the Levi-Civita field. Zbl 1428.46048
Flynn, Darren; Shamseddine, Khodr
2018
Towards three-dimensional conformal probability. Zbl 1420.81023
Abdesselam, Abdelmalek
2018
Biology as a constructive physics. Zbl 1419.92022
Kozyrev, S. V.
2018
On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over $$p$$-adic field. Zbl 07090162
Pourhadi, Ehsan; Khrennikov, A. Yu.
2018
A transfer principle for the continuations of real functions to the Levi-Civita field. Zbl 1415.26006
Bottazzi, Emanuele
2018
Some problems in the theory of approximation of functions on the group of $$p$$-adic numbers. Zbl 1411.46053
Platonov, Sergey S.
2018
On the classification of $$p$$-adic UHF Banach algebras. Zbl 1428.46046
Baker, R. L.
2018
A possible $$p$$-adic Weber-Fechner law. Zbl 1422.91631
Iurato, Giuseppe
2018
Generalized $$p$$-adic Fourier transform and estimates of integral modulus of continuity in terms of this transform. Zbl 1432.30033
Volosivets, S. S.; Kuznetsova, M. A.
2018
Solvability of a class of nonlinear pseudo-differential equations in $$\mathbb{R}^n$$. Zbl 1402.35325
Khachatryan, A. Kh.; Khachatryan, Kh. A.
2018
Model of $$p$$-adic random walk in a potential. Zbl 1402.60052
Bikulov, A. Kh.; Zubarev, A. P.
2018
$$p$$-adic mathematical physics: the first 30 years. Zbl 1394.81009
Dragovich, B.; Khrennikov, A. Yu.; Kozyrev, S. V.; Volovich, I. V.; Zelenov, E. I.
2017
Weak and strong estimates for rough Hausdorff type operator defined on $$p$$-adic linear space. Zbl 06847852
Volosivets, S. S.
2017
On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains. Zbl 1375.31010
Matevossian, Hovik A.
2017
Trees and ultrametric Möbius structures. Zbl 1387.53022
Beyrer, Jonas; Schroeder, Victor
2017
The comb representation of compact ultrametric spaces. Zbl 1379.54023
Lambert, Amaury; Uribe Bravo, Gerónimo
2017
An analogue of the Titchmarsh theorem for the Fourier transform on the group of $$p$$-adic numbers. Zbl 1409.11116
Platonov, Sergey S.
2017
An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups. Zbl 1388.43004
Platonov, Sergey S.
2017
Self-adjoint approximations of the degenerate Schrödinger operator. Zbl 06725606
Sakbaev, V. Zh.; Volovich, I. V.
2017
Local zeta functions, pseudodifferential operators and Sobolev-type spaces over non-Archimedean local fields. Zbl 1427.11135
Zúñiga-Galindo, W. A.
2017
Generalized fractional integrals in $$p$$-adic Morrey and Herz spaces. Zbl 1410.46058
Volosivets, S. S.
2017
On solvability of one class of nonlinear integral equations on whole line with a weak singularity at zero. Zbl 1390.45011
Khachatryan, Khachatur A.
2017
Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field. Zbl 1367.30034
Vu Hoai An; Pham Ngoc Hoa; Ha Huy Khoai
2017
The $$p$$-adic order of the $$k$$-Fibonacci and $$k$$-Lucas numbers. Zbl 1396.11038
Kreutz, A.; Lelis, J.; Marques, D.; Silva, E.; Trojovský, P.
2017
Blow-up phenomena for $$p$$-adic semilinear heat equations. Zbl 1387.35318
Chacón-Cortés, Leonardo F.; Vargas, Andrés
2017
On the topological structure of a mathematical model of human unconscious. Zbl 1414.91313
Iurato, Giuseppe; Khrennikov, Andrei
2017
A heat equation on some adic completions of $$\mathbb{Q}$$ and ultrametric analysis. Zbl 1393.46058
Aguilar-Arteaga, V. A.; Cruz-López, M.; Estala-Arias, S.
2017
$$q$$-deformations of statistical mechanical systems and motives over finite fields. Zbl 1386.82006
Marcolli, Matilde; Ren, Zhi
2017
The $$p$$-adic order of some fibonomial coefficients whose entries are powers of $$p$$. Zbl 1416.11031
Trojovský, Pavel
2017
Limit theorems for $$p$$-adic valued asymmetric semistable laws and processes. Zbl 1381.60090
Yasuda, Kumi
2017
$$p$$-adic mathematical physics and B. Dragovich research. Zbl 1364.81008
Aref&rsquo;eva, I. Ya.; Djordjevic, G. S.; Khrennikov, A. Yu.; Kozyrev, S. V.; Rakic, Z.; Volovich, I. V.
2017
The $$p$$-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space. Zbl 1369.47080
Chuong, N. M.; Duong, D. V.
2016
Order, type and cotype of growth for $$p$$-adic entire functions: a survey with additional properties. Zbl 1432.30031
Boussaf, Kamal; Boutabaa, Abdelbaki; Escassut, Alain
2016
On periodic Gibbs measures of $$p$$-adic Potts model on a Cayley tree. Zbl 1356.82022
Mukhamedov, F.; Khakimov, O.
2016
Invariant ultrametrics and Markov processes on the finite adèle ring of $$\mathbb{Q}$$. Zbl 1370.11127
Cruz-López, Manuel; Estala-Arias, Samuel
2016
Formal foundations for the origins of human consciousness. Zbl 1407.91210
Iurato, Giuseppe; Khrennikov, Andrei; Murtagh, F.
2016
Bounds of $$p$$-adic weighted Hardy-Cesàro operators and their commutators on $$p$$-adic weighted spaces of Morrey types. Zbl 1371.42015
Nguyen Minh Chuong; Ha Duy Hung; Nguyen Thi Hong
2016
Ultrametricity indices for the Euclidean and Boolean hypercubes. Zbl 06844448
2016
$$p$$-adic probability logics. Zbl 1353.03013
Ilić Stepić, A.; Ognjanović, Z.; Ikodinović, N.; Perović, A.
2016
The corona problem on a complete ultrametric algebraically closed field. Zbl 1353.46056
Escassut, Alain
2016
Ergodic polynomials on subsets of $$p$$-adic integers. Zbl 1347.37146
Memić, N.
2016
Exceptional Lie algebras at the very foundations of space and time. Zbl 1357.81160
Marrani, A.; Truini, P.
2016
Painlevé VI equations in $$p$$-adic time. Zbl 1433.14018
Manin, Yu. I.
2016
Sparse $$p$$-adic data coding for computationally efficient and effective big data analytics. Zbl 1353.94026
Murtagh, F.
2016
A local mean value theorem for functions on non-Archimedean field extensions of the real numbers. Zbl 1345.26042
Shamseddine, K.; Bookatz, G.
2016
KMS weights on higher rank buildings. Zbl 1392.46059
Marcinek, J.; Marcolli, M.
2016
Model of protein fragments and statistical potentials. Zbl 1383.92059
Kozyrev, S. V.
2016
On spaces extremal for the Gomory-Hu inequality. Zbl 1343.05072
Dovgoshey, O.; Petrov, E.; Teichert, H.-M.
2015
Some pathways in non-linear supersymmetry: special geometry Born-Infeld’s, cosmology and dualities. Zbl 1337.81069
Ferrara, Sergio; Sagnotti, A.
2015
On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains. Zbl 1325.35032
Matevossian, H. A.
2015
Hysteresis model of unconscious-conscious interconnection: exploring dynamics on $$m$$-adic trees. Zbl 1336.91061
Iurato, Giuseppe; Khrennikov, Andrei
2015
$$p$$-adic (3, 2)-rational dynamical systems. Zbl 1347.37149
Sattarov, I. A.
2015
The $$p$$-adic analytic subgroup theorem revisited. Zbl 1327.11049
Fuchs, C.; Pham, D. H.
2015
Application of $$p$$-adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into $$\mathbb{Q}_p$$. Zbl 1323.60098
Bikulov, A. Kh.; Zubarev, A. P.
2015
Functional stochastic classical mechanics. Zbl 1367.70002
Volovich, I. V.
2015
Freudenthal duality in gravity: from groups of type $$E_{7}$$ to pre-homogeneous spaces. Zbl 1339.83074
Marrani, Alessio
2015
Quantization causes waves: smooth finitely computable functions are affine. Zbl 1328.81136
Anashin, V. S.
2015
Parabolic-type pseudodifferential equations with elliptic symbols in dimension 3 over $$p$$-adics. Zbl 1330.35231
Casas-Sánchez, O. F.; Galeano-Peñaloza, J.; Rodriguez-Vega, J. J.
2015
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### Cited by 606 Authors

 59 Khrennikov, Andreĭ Yur’evich 26 Kozyrev, Sergeĭ Vladimirovich 25 Mukhamedov, Farruh Maksutovich 24 Dragovich, Branko 24 Zúñiga-Galindo, Wilson A. 18 Dovgoshey, Oleksiy Alfredovich 15 Duong, Dao Van 14 Matevosyan, Hovik A. 14 Volovich, Igor’ Vasil’evich 13 Khakimov, Otabek N. 12 Marcolli, Matilde 11 Nguyen Minh Chuong 11 Rozikov, Utkir A. 11 Volosivets, Sergeĭ Sergeevich 10 Albeverio, Sergio A. 10 Memić, Nacima 10 Petrov, Evgenii Aleksandrovich 10 Sergeev, Yaroslav Dmitrievich 10 Zubarev, Aleksandr Petrovich 9 Hussain, Amjad 9 Jeong, Sangtae 9 Sakbaev, Vsevolod Zhanovich 9 Sarfraz, Naqash 8 Chacón-Cortes, Leonardo Fabio 8 Rakić, Zoran 8 Torresblanca-Badillo, Anselmo 8 Trushechkin, Anton Sergeevich 8 Vladimirov, Vasiliĭ Sergeevich 8 Zelenov, Evgenii I. 7 Bradley, Patrick Erik 7 Dung, Kieu Huu 7 Estala-Arias, Samuel 7 Farkov, Yuriĭ Anatol’evich 7 Liao, Lingmin 7 Shelkovich, Vladimir M. 7 Varadarajan, Veeravalli S. 6 Bikulov, Al’bert Khakimovich 6 Cruz-López, Manuel 6 Dimitrijevic, Ivan 6 Fan, Shilei 6 Sattarov, Iskandar A. 6 Stankovic, Jelena 5 Anashin, Vladimir Sergeevich 5 Biswas, Tanmay 5 Casas-Sánchez, Oscar Francisco 5 Escassut, Alain 5 Galeano-Peñaloza, Jeanneth 5 Iurato, Giuseppe 5 Lapidus, Michel L. 5 Mišić, Nataša Ž. 5 Murtagh, Fionn D. 5 Oleschko, Klaudia 5 Platonov, Sergei S. 5 Weisbart, David 5 Yurova, Ekaterina I. 4 Ahmad, Owais 4 Aref’eva, Irina Yaroslavna 4 De Leone, Renato 4 Digernes, Trond 4 Ferrara, Sergio 4 Gutiérrez García, Ismael Segundo 4 Jarad, Fahd 4 Khachatryan, Khachatur Aghavardovich 4 Kosyak, Alexandre V. 4 Kronberg, D. A. 4 Lambert, Amaury 4 Lukomskiĭ, Sergeĭ Fedorovich 4 Marrani, Alessio 4 Pathak, Ashish 4 Singh, Guru P. 4 Skopina, Maria A. 3 Accardi, Luigi 3 Aguilar-Arteaga, Victor A. 3 Behera, Biswaranjan 3 Biswas, Chinmay 3 Bottazzi, Emanuele 3 Caterina, Gianluca 3 Daher, Radouan 3 D’Alotto, Louis A. 3 Doğan, Mutlay 3 Drozhzhinov, Yuriĭ Nikolaevich 3 Fan, Ai Hua 3 Fioresi, Rita 3 Gangle, Rocco 3 Jahan, Qaiser 3 Kochubeĭ, Anatoliĭ Naumovych 3 Koshelev, Alexey S. 3 Li, Chunlan 3 Manin, Yuri Ivanovich 3 Missarov, Mukadas D. 3 Pourhadi, Ehsan 3 Rodríguez Vega, John Jaime 3 Saburov, Mansoor 3 Sagnotti, Augusto 3 Santocanale, Luigi 3 Sawano, Yoshihiro 3 Schumann, Andrew 3 Shamseddine, Khodr 3 Sheikh, Neyaz Ahmad 3 Shimomura, Tetsu ...and 506 more Authors
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### Cited in 199 Journals

 174 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 29 Theoretical and Mathematical Physics 23 Proceedings of the Steklov Institute of Mathematics 20 Journal of Mathematical Analysis and Applications 14 Applied Mathematics and Computation 12 Journal of High Energy Physics 11 Journal of Number Theory 10 Journal of Mathematical Sciences (New York) 10 Lobachevskii Journal of Mathematics 9 Doklady Mathematics 8 Mathematical Notes 8 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 7 Communications in Mathematical Physics 7 Journal of Mathematical Physics 7 Indagationes Mathematicae. New Series 7 The Journal of Fourier Analysis and Applications 7 Journal of Inequalities and Applications 7 Journal of Pseudo-Differential Operators and Applications 6 Physica A 6 Reports on Mathematical Physics 6 Russian Journal of Mathematical Physics 6 Infinite Dimensional Analysis, Quantum Probability and Related Topics 6 Foundations of Physics 6 Journal of Function Spaces 5 Filomat 5 Mathematical Physics, Analysis and Geometry 5 Soft Computing 4 Physics Letters. B 4 Ukrainian Mathematical Journal 4 Reviews in Mathematical Physics 4 Chaos, Solitons and Fractals 4 Journal of Classification 4 Finite Fields and their Applications 4 Discrete and Continuous Dynamical Systems 4 Differential Equations 4 International Journal of Number Theory 3 Journal of Statistical Physics 3 Letters in Mathematical Physics 3 Nuclear Physics. B 3 Journal of Geometry and Physics 3 Advances in Mathematics 3 Journal of Computational and Applied Mathematics 3 Results in Mathematics 3 Siberian Mathematical Journal 3 Topology and its Applications 3 Statistics & Probability Letters 3 Izvestiya: Mathematics 3 Communications in Nonlinear Science and Numerical Simulation 3 International Journal of Wavelets, Multiresolution and Information Processing 3 Complex Analysis and Operator Theory 3 Journal of Noncommutative Geometry 3 Tbilisi Mathematical Journal 3 Analysis and Mathematical Physics 3 Advances in Operator Theory 3 Korean Journal of Mathematics 2 International Journal of Modern Physics A 2 Analysis Mathematica 2 International Journal of Theoretical Physics 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 The Annals of Applied Probability 2 Computational Mathematics and Mathematical Physics 2 Expositiones Mathematicae 2 Russian Mathematics 2 Applied Categorical Structures 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 Georgian Mathematical Journal 2 Selecta Mathematica. New Series 2 Transformation Groups 2 Matematychni Studiï 2 Dynamical Systems 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Central European Journal of Mathematics 2 Mediterranean Journal of Mathematics 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Complex Variables and Elliptic Equations 2 Frontiers of Mathematics in China 2 Journal of Mathematical Inequalities 2 Kinetic and Related Models 2 Science China. Mathematics 2 International Journal of Applied and Computational Mathematics 2 Open Mathematics 2 Journal of Siberian Federal University. Mathematics & Physics 2 AIMS Mathematics 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 International Journal of General Systems 1 Nonlinearity 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Acta Mathematica Vietnamica 1 Archiv der Mathematik 1 Collectanea Mathematica 1 Colloquium Mathematicum 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Approximation Theory 1 Journal of Differential Equations ...and 99 more Journals
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### Cited in 59 Fields

 170 Number theory (11-XX) 116 Harmonic analysis on Euclidean spaces (42-XX) 116 Functional analysis (46-XX) 112 Quantum theory (81-XX) 86 Dynamical systems and ergodic theory (37-XX) 83 Operator theory (47-XX) 76 Partial differential equations (35-XX) 74 Statistical mechanics, structure of matter (82-XX) 71 Probability theory and stochastic processes (60-XX) 50 Real functions (26-XX) 44 General topology (54-XX) 37 Biology and other natural sciences (92-XX) 36 Combinatorics (05-XX) 33 Computer science (68-XX) 32 Field theory and polynomials (12-XX) 30 Abstract harmonic analysis (43-XX) 28 Functions of a complex variable (30-XX) 27 Relativity and gravitational theory (83-XX) 23 Mathematical logic and foundations (03-XX) 23 Algebraic geometry (14-XX) 20 Topological groups, Lie groups (22-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Numerical analysis (65-XX) 16 Potential theory (31-XX) 15 Differential geometry (53-XX) 14 Nonassociative rings and algebras (17-XX) 13 Measure and integration (28-XX) 12 Statistics (62-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Group theory and generalizations (20-XX) 11 Information and communication theory, circuits (94-XX) 10 Sequences, series, summability (40-XX) 9 Mechanics of particles and systems (70-XX) 9 Operations research, mathematical programming (90-XX) 8 Several complex variables and analytic spaces (32-XX) 8 Difference and functional equations (39-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 Associative rings and algebras (16-XX) 7 Ordinary differential equations (34-XX) 6 Integral equations (45-XX) 6 Geometry (51-XX) 5 History and biography (01-XX) 5 Category theory; homological algebra (18-XX) 5 Approximations and expansions (41-XX) 5 Fluid mechanics (76-XX) 4 General algebraic systems (08-XX) 4 Commutative algebra (13-XX) 4 $$K$$-theory (19-XX) 4 Algebraic topology (55-XX) 3 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Manifolds and cell complexes (57-XX) 3 Astronomy and astrophysics (85-XX) 2 Special functions (33-XX) 2 Mechanics of deformable solids (74-XX) 2 Systems theory; control (93-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)