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Record Nr. |
UNINA9910974261603321 |
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Autore |
Chen Zhen-Qing |
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Titolo |
Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2021 |
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©2021 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (102 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.271 |
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Classificazione |
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60J3535K0860J7531C2560J2560J45 |
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Altri autori (Persone) |
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KumagaiTakashi |
WangJian <1979-> |
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Disciplina |
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Soggetti |
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Kernel functions |
Probability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolvents |
Partial differential equations -- Parabolic equations and systems -- Heat kernel |
Probability theory and stochastic processes -- Markov processes -- Jump processes |
Potential theory -- Other generalizations -- Dirichlet spaces |
Probability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces |
Probability theory and stochastic processes -- Markov processes -- Probabilistic potential theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Cover -- Title page -- Chapter 1. Introduction and Main Results -- 1. Setting -- 2. Heat kernel -- Chapter 2. Preliminaries -- Chapter 3. Implications of heat kernel estimates -- 1. \UHK( )+(\sE,\sF) ⟹\J_{ ,≤}, and \HK( )⟹\Jᵩ -- 2. \UHK( ) (\sE,\sF) ⟹\SCSJ( ) -- Chapter 4. Implications of \CSJ( ) and \J_{ ,≥} -- 1. \J_{ ,≥}⟹\FK( ) -- 2. Caccioppoli and ¹-mean value inequalities -- 3. \FK( )+\J_{ ,≤}+\CSJ( )⟹\Eᵩ -- 4. \FK( )+\Eᵩ+\J_{ ,≤}⟹\UHKD( ) -- Chapter 5. Consequences of condition \Jᵩ and mean exit time condition \Eᵩ -- 1. \UHKD( )+\J_{ ,≤}+\Eᵩ⟹\UHK( ), \Jᵩ+\Eᵩ⟹\UHK( ) -- 2. \Jᵩ+\Eᵩ⟹\LHK( ) -- Chapter 6. Applications and Examples -- 1. Applications -- 2. Counterexample |
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-- Chapter 7. Appendix -- 1. Lévy system formula -- 2. Meyer's decomposition -- 3. Some results related to \FK( ). -- 4. Some results related to (Dirichlet) heat kernel -- 5. \SCSJ( )+\J_{ ,≤}⟹(\sE,\sF) is conservative -- Acknowledgment -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for -stable-like processes even with 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area"-- |
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