04652nam 22006853 450 991097426160332120250626111448.097814704663811470466384(CKB)4940000000609986(MiAaPQ)EBC6715036(Au-PeEL)EBL6715036(RPAM)22487688(PPN)258258632(OCoLC)1266906499(EXLCZ)99494000000060998620210901d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (102 pages)Memoirs of the American Mathematical Society ;v.2719781470448639 1470448637 Includes bibliographical references.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 -- 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."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"--Provided by publisher.Memoirs of the American Mathematical SocietyKernel functionsProbability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolventsmscPartial differential equations -- Parabolic equations and systems -- Heat kernelmscProbability theory and stochastic processes -- Markov processes -- Jump processesmscPotential theory -- Other generalizations -- Dirichlet spacesmscProbability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spacesmscProbability theory and stochastic processes -- Markov processes -- Probabilistic potential theorymscKernel 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.519.2/3360J3535K0860J7531C2560J2560J45mscChen Zhen-Qing514801Kumagai Takashi525017Wang Jian1979-1829921MiAaPQMiAaPQMiAaPQBOOK9910974261603321Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms4400060UNINA