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## Kigami, Jun

Compute Distance To:
 Author ID: kigami.jun Published as: Kigami, Jun; Kigami, J.
 Documents Indexed: 37 Publications since 1983, including 7 Books
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#### Co-Authors

 26 single-authored 2 Lapidus, Michel L. 2 Strichartz, Robert S. 2 Yamaguti, Masaya 1 Alonso-Ruiz, Patricia 1 Barlow, Martin T. 1 Freiberg, Uta Renata 1 Hambly, Ben M. 1 Hata, Masayoshi 1 Kumagai, Takashi 1 Oba, Takuji 1 Sheldon, Daniel R. 1 Walker, Katharine C.
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#### Serials

 3 Journal of Functional Analysis 3 Memoirs of the American Mathematical Society 2 Communications in Mathematical Physics 2 Journal of Mathematical Biology 2 Mathematical Proceedings of the Cambridge Philosophical Society 1 Advances in Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematics of Kyoto University 1 Journal of the Mathematical Society of Japan 1 Mathematische Annalen 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Japan Journal of Applied Mathematics 1 Sūgaku 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Experimental Mathematics 1 Fractals 1 Journal of Mathematical Sciences. University of Tokyo 1 Cambridge Tracts in Mathematics 1 Lecture Notes in Mathematics 1 Translations of Mathematical Monographs 1 Translations. Series 2. American Mathematical Society 1 Journal of Fractal Geometry
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#### Fields

 23 Measure and integration (28-XX) 16 Potential theory (31-XX) 15 Probability theory and stochastic processes (60-XX) 10 Partial differential equations (35-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Dynamical systems and ergodic theory (37-XX) 3 Functions of a complex variable (30-XX) 3 Biology and other natural sciences (92-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX)

#### Citations contained in zbMATH Open

34 Publications have been cited 1,177 times in 574 Documents Cited by Year
Analysis on fractals. Zbl 0998.28004
Kigami, Jun
2001
Harmonic calculus on P.C.F. self-similar sets. Zbl 0773.31009
Kigami, Jun
1993
A harmonic calculus on the Sierpiński spaces. Zbl 0686.31003
Kigami, Jun
1989
Weyl’s problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals. Zbl 0806.35130
Kigami, Jun; Lapidus, Michel L.
1993
Harmonic analysis for resistance forms. Zbl 1039.31014
Kigami, Jun
2003
Resistance forms, quasisymmetric maps and heat kernel estimates. Zbl 1246.60099
Kigami, Jun
2012
Localized eigenfunctions of the Laplacian on p. c. f. self-similar sets. Zbl 0904.35064
Barlow, Martin T.; Kigami, Jun
1997
Harmonic calculus on limits of networks and its application to dendrites. Zbl 0820.60060
Kigami, Jun
1995
Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate. Zbl 1143.28004
Kigami, Jun
2008
Harmonic metric and Dirichlet form on the Sierpinski gasket. Zbl 0793.31005
Kigami, J.
1993
Volume doubling measures and heat kernel estimates on self-similar sets. Zbl 1181.28011
Kigami, Jun
2009
Local Nash inequality and inhomogeneity of heat kernels. Zbl 1060.60076
Kigami, Jun
2004
Effective resistances for harmonic structures on p.c.f. self-similar sets. Zbl 0803.60074
Kigami, Jun
1994
Mathematics of fractals. Transl. from the Japanese by Kiki Hudson. Zbl 0888.58030
Yamaguti, Masaya; Hata, Masayoshi; Kigami, Jun
1997
Self-similarity of volume measures for Laplacians on p. c. f. self-similar fractals. Zbl 0983.35097
Kigami, Jun; Lapidus, Michel L.
2001
Distributions of localized eigenvalues of Laplacians on post critically finite self-similar sets. Zbl 0908.35087
Kigami, Jun
1998
Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees. Zbl 1234.60077
Kigami, Jun
2010
Analysis on fractals. Paperback reprint of the hardback edition 2001. Zbl 1143.28005
Kigami, Jun
2008
Green’s functions on fractals. Zbl 0983.31005
Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S.
2000
Constructing a Laplacian on the diamond fractal. Zbl 0999.31007
Kigami, Jun; Strichartz, Robert S.; Walker, Katharine C.
2001
Transitions on a noncompact Cantor set and random walks on its defining tree. Zbl 1286.31006
Kigami, Jun
2013
Hausdorff dimensions of self-similar sets and shortest path metrics. Zbl 0851.28002
Kigami, Jun
1995
Laplacians on self-similar sets and their spectral distributions. Zbl 0871.28008
Kigami, Jun
1995
Completely symmetric resistance forms on the stretched Sierpiński gasket. Zbl 1397.31003
Ruiz, Patricia Alonso; Freiberg, Uta R.; Kigami, Jun
2018
Multifractal formalisms for the local spectral and walk dimensions. Zbl 1002.60064
Hambly, B. M.; Kigami, Jun; Kumagai, Takashi
2002
The dynamical attainability of ESS in evolutionary games. Zbl 0734.92021
1991
Quasisymmetric modification of metrics on self-similar sets. Zbl 1318.28028
Kigami, Jun
2014
Why does invasion imply substitution? Beyond the paradigm of invasion fitness. Zbl 1400.92374
Oba, Takuji; Kigami, Jun
2018
Some remarks on Dirichlet problem of Poisson equation. Zbl 0672.35018
Yamaguti, Masaya; Kigami, Jun
1988
Time changes of the Brownian motion: Poincaré inequality, heat kernel estimate and protodistance. Zbl 1448.60003
Kigami, Jun
2019
Markov property of Kusuoka-Zhou’s Dirichlet forms on self-similar sets. Zbl 0964.60079
Kigami, Jun
2000
On Laplacians on self-similar sets. Analysis on fractals. Zbl 0754.58024
Kigami, Jun
1992
Some functional equations which generate both crinkly broken lines and curves. Zbl 0639.30025
Kigami, Jun
1987
Geometry and analysis of metric spaces via weighted partitions. Zbl 1455.28001
Kigami, Jun
2020
Geometry and analysis of metric spaces via weighted partitions. Zbl 1455.28001
Kigami, Jun
2020
Time changes of the Brownian motion: Poincaré inequality, heat kernel estimate and protodistance. Zbl 1448.60003
Kigami, Jun
2019
Completely symmetric resistance forms on the stretched Sierpiński gasket. Zbl 1397.31003
Ruiz, Patricia Alonso; Freiberg, Uta R.; Kigami, Jun
2018
Why does invasion imply substitution? Beyond the paradigm of invasion fitness. Zbl 1400.92374
Oba, Takuji; Kigami, Jun
2018
Quasisymmetric modification of metrics on self-similar sets. Zbl 1318.28028
Kigami, Jun
2014
Transitions on a noncompact Cantor set and random walks on its defining tree. Zbl 1286.31006
Kigami, Jun
2013
Resistance forms, quasisymmetric maps and heat kernel estimates. Zbl 1246.60099
Kigami, Jun
2012
Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees. Zbl 1234.60077
Kigami, Jun
2010
Volume doubling measures and heat kernel estimates on self-similar sets. Zbl 1181.28011
Kigami, Jun
2009
Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate. Zbl 1143.28004
Kigami, Jun
2008
Analysis on fractals. Paperback reprint of the hardback edition 2001. Zbl 1143.28005
Kigami, Jun
2008
Local Nash inequality and inhomogeneity of heat kernels. Zbl 1060.60076
Kigami, Jun
2004
Harmonic analysis for resistance forms. Zbl 1039.31014
Kigami, Jun
2003
Multifractal formalisms for the local spectral and walk dimensions. Zbl 1002.60064
Hambly, B. M.; Kigami, Jun; Kumagai, Takashi
2002
Analysis on fractals. Zbl 0998.28004
Kigami, Jun
2001
Self-similarity of volume measures for Laplacians on p. c. f. self-similar fractals. Zbl 0983.35097
Kigami, Jun; Lapidus, Michel L.
2001
Constructing a Laplacian on the diamond fractal. Zbl 0999.31007
Kigami, Jun; Strichartz, Robert S.; Walker, Katharine C.
2001
Green’s functions on fractals. Zbl 0983.31005
Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S.
2000
Markov property of Kusuoka-Zhou’s Dirichlet forms on self-similar sets. Zbl 0964.60079
Kigami, Jun
2000
Distributions of localized eigenvalues of Laplacians on post critically finite self-similar sets. Zbl 0908.35087
Kigami, Jun
1998
Localized eigenfunctions of the Laplacian on p. c. f. self-similar sets. Zbl 0904.35064
Barlow, Martin T.; Kigami, Jun
1997
Mathematics of fractals. Transl. from the Japanese by Kiki Hudson. Zbl 0888.58030
Yamaguti, Masaya; Hata, Masayoshi; Kigami, Jun
1997
Harmonic calculus on limits of networks and its application to dendrites. Zbl 0820.60060
Kigami, Jun
1995
Hausdorff dimensions of self-similar sets and shortest path metrics. Zbl 0851.28002
Kigami, Jun
1995
Laplacians on self-similar sets and their spectral distributions. Zbl 0871.28008
Kigami, Jun
1995
Effective resistances for harmonic structures on p.c.f. self-similar sets. Zbl 0803.60074
Kigami, Jun
1994
Harmonic calculus on P.C.F. self-similar sets. Zbl 0773.31009
Kigami, Jun
1993
Weyl’s problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals. Zbl 0806.35130
Kigami, Jun; Lapidus, Michel L.
1993
Harmonic metric and Dirichlet form on the Sierpinski gasket. Zbl 0793.31005
Kigami, J.
1993
On Laplacians on self-similar sets. Analysis on fractals. Zbl 0754.58024
Kigami, Jun
1992
The dynamical attainability of ESS in evolutionary games. Zbl 0734.92021
1991
A harmonic calculus on the Sierpiński spaces. Zbl 0686.31003
Kigami, Jun
1989
Some remarks on Dirichlet problem of Poisson equation. Zbl 0672.35018
Yamaguti, Masaya; Kigami, Jun
1988
Some functional equations which generate both crinkly broken lines and curves. Zbl 0639.30025
Kigami, Jun
1987
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#### Cited by 583 Authors

 54 Strichartz, Robert S. 31 Teplyaev, Alexander 17 Jørgensen, Palle E. T. 17 Kumagai, Takashi 15 Lau, Kasing 15 Rogers, Luke G. 14 Hambly, Ben M. 14 Hu, Jiaxin 13 Hinz, Michael 13 Kigami, Jun 12 Croydon, David A. 12 Grigor’yan, Alexander Asaturovich 10 Freiberg, Uta Renata 10 Qiu, Hua 9 Dutkay, Dorin Ervin 9 Ionescu, Marius V. 9 Lapidus, Michel L. 8 Cipriani, Fabio 8 Golmankhaneh, Alireza Khalili 8 Hino, Masanori 8 Metz, Volker 8 Ngai, Sze-Man 7 Alonso-Ruiz, Patricia 7 Cao, Shiping 7 Kajino, Naotaka 7 Okoudjou, Kasso A. 6 Mihail, Alexandru 6 Pearse, Erin Peter James 6 Ruan, Huo-Jun 6 Sauvageot, Jean-Luc 6 Steinhurst, Benjamin 6 Zähle, Martina 5 Barlow, Martin T. 5 Breckner, Brigitte Erika 5 Guido, Daniele 5 Isola, Tommaso 5 Kelleher, Daniel J. 5 Peirone, Roberto 5 Rastegaev, N. V. 5 Teufl, Elmar 5 Wang, Xiangyang 5 Xi, Lifeng 4 Angulo, José Miguel 4 Anh, Vo V. 4 Baudoin, Fabrice 4 Capitanelli, Raffaela 4 David, Claire 4 Grabner, Peter J. 4 Gu, Qingsong 4 Lancia, Maria Rosaria 4 Miculescu, Radu 4 Özdemir, Yunus 4 Priyadarshi, Amit 4 Ruiz-Medina, María Dolores 4 Sahu, Abhilash 4 Shanmugalingam, Nageswari 4 Shima, Tadashi 4 Tang, Donglei 4 Tyson, Jeremy T. 4 Wagner, Stephan G. 3 Achdou, Yves 3 Aerts, Diederik Emiel 3 Băleanu, Dumitru I. 3 Barnsley, Michael Fielding 3 Chen, Joe Po-Chou 3 Cho, Ilwoo 3 Czachor, Marek 3 De Amo, Enrique 3 Demir, Bunyamin 3 Diaz Carrillo, Manuel 3 Fernández-Sánchez, Juan 3 Gangal, Anil D. 3 Georgakopoulos, Agelos 3 Golmankhaneh, Ali Khalili 3 Gu, Jiangwen 3 Kaneko, Hiroshi 3 Kasue, Atsushi 3 Keller, Matthias 3 Kesseböhmer, Marc 3 Koçak, Şahin 3 Krön, Bernhard 3 Kuna, Maciej 3 Lai, Chun-Kit 3 Mosco, Umberto 3 Mulholland, Anthony J. 3 Murugan, Mathav Kishore 3 Ostoja-Starzewski, Martin 3 Parvate, Abhay 3 Rădulescu, Vicenţiu D. 3 Riane, Nizar 3 Samuel, Tony 3 Sekiguchi, Takeshi 3 Shiota, Yasunobu 3 Sikora, Adam S. 3 Tang, Wei 3 Tchou, Nicoletta Anna 3 Telcs, András 3 Tetenov, Andreĭ Viktorovich 3 Triebel, Hans 3 Varga, Csaba György ...and 483 more Authors
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#### Cited in 176 Serials

 38 Journal of Functional Analysis 29 Transactions of the American Mathematical Society 29 Fractals 18 Journal of Mathematical Analysis and Applications 15 Advances in Mathematics 15 Potential Analysis 15 The Journal of Fourier Analysis and Applications 14 Chaos, Solitons and Fractals 12 Acta Applicandae Mathematicae 12 Journal of Fractal Geometry 11 Communications in Mathematical Physics 11 Probability Theory and Related Fields 9 Journal d’Analyse Mathématique 9 Proceedings of the American Mathematical Society 9 Stochastic Processes and their Applications 9 Communications on Pure and Applied Analysis 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Journal of Theoretical Probability 6 Monatshefte für Mathematik 6 Zeitschrift für Analysis und ihre Anwendungen 6 Forum Mathematicum 5 Rocky Mountain Journal of Mathematics 5 The Annals of Probability 5 Mathematische Nachrichten 5 Mathematische Zeitschrift 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Experimental Mathematics 4 Journal of Mathematical Biology 4 Journal of Mathematical Physics 4 Mathematische Annalen 4 Topology and its Applications 4 Constructive Approximation 4 Japan Journal of Industrial and Applied Mathematics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Linear Algebra and its Applications 4 Journal of Mathematical Sciences (New York) 4 Electronic Journal of Probability 4 Communications in Nonlinear Science and Numerical Simulation 4 Complex Analysis and Operator Theory 3 Nonlinearity 3 Memoirs of the American Mathematical Society 3 Osaka Journal of Mathematics 3 Stochastic Analysis and Applications 3 Revista Matemática Iberoamericana 3 Discrete and Continuous Dynamical Systems 3 Analysis (München) 3 Acta Mathematica Sinica. English Series 3 Nonlinear Analysis. Real World Applications 3 Mediterranean Journal of Mathematics 3 Fixed Point Theory and Applications 3 Complex Variables and Elliptic Equations 3 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Modern Physics Letters A 2 Advances in Applied Probability 2 International Journal of Theoretical Physics 2 Journal of Statistical Physics 2 Letters in Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Physics Letters. A 2 Annales de l’Institut Fourier 2 Archiv der Mathematik 2 Demonstratio Mathematica 2 Functional Analysis and its Applications 2 Illinois Journal of Mathematics 2 Journal of Approximation Theory 2 Journal für die Reine und Angewandte Mathematik 2 Tohoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Japan Journal of Applied Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Calculus of Variations and Partial Differential Equations 2 Advances in Applied Clifford Algebras 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Mathematical Inequalities & Applications 2 Annals of Mathematics. Second Series 2 Journal of the Australian Mathematical Society 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Proceedings of the Steklov Institute of Mathematics 1 International Journal of Modern Physics B 1 Acta Mechanica 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 International Journal of Engineering Science 1 International Journal of Solids and Structures 1 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Reports on Mathematical Physics 1 Studia Mathematica 1 Arkiv för Matematik 1 Mathematics of Computation 1 Journal of Geometry and Physics 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV ...and 76 more Serials
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#### Cited in 50 Fields

 352 Measure and integration (28-XX) 177 Probability theory and stochastic processes (60-XX) 130 Potential theory (31-XX) 116 Partial differential equations (35-XX) 86 Operator theory (47-XX) 71 Functional analysis (46-XX) 45 Dynamical systems and ergodic theory (37-XX) 43 Combinatorics (05-XX) 39 Harmonic analysis on Euclidean spaces (42-XX) 35 Real functions (26-XX) 30 Global analysis, analysis on manifolds (58-XX) 25 Quantum theory (81-XX) 23 Statistical mechanics, structure of matter (82-XX) 21 Ordinary differential equations (34-XX) 18 Functions of a complex variable (30-XX) 17 Number theory (11-XX) 15 General topology (54-XX) 14 Differential geometry (53-XX) 11 Difference and functional equations (39-XX) 10 Numerical analysis (65-XX) 9 Abstract harmonic analysis (43-XX) 9 Biology and other natural sciences (92-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Information and communication theory, circuits (94-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Group theory and generalizations (20-XX) 5 Computer science (68-XX) 5 Mechanics of deformable solids (74-XX) 4 Special functions (33-XX) 4 Geometry (51-XX) 4 Statistics (62-XX) 4 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Topological groups, Lie groups (22-XX) 3 Approximations and expansions (41-XX) 3 Convex and discrete geometry (52-XX) 3 Optics, electromagnetic theory (78-XX) 2 Integral equations (45-XX) 2 Manifolds and cell complexes (57-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)