03005nam 2200589 450 991081173590332120170816143240.01-4704-0538-5(CKB)3360000000465116(EBL)3114097(SSID)ssj0000889299(PQKBManifestationID)11475769(PQKBTitleCode)TC0000889299(PQKBWorkID)10875545(PQKB)10835711(MiAaPQ)EBC3114097(RPAM)15573156(PPN)195418212(EXLCZ)99336000000046511620150417h20092009 uy 0engur|n|---|||||txtccrVolume doubling measures and heat kernel estimates on self-similar sets /Jun KigamiProvidence, Rhode Island :American Mathematical Society,2009.©20091 online resource (110 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 199, Number 932"Volume 199, Number 932 (third of 6 numbers)."0-8218-4292-7 Includes bibliographical references and index.""Contents""; ""Prologue""; ""0.1. Introduction""; ""0.2. the Unit square""; ""Chapter 1. Scales and Volume Doubling Property of Measures""; ""1.1. Scale""; ""1.2. Self-similar structures and measures""; ""1.3. Volume doubling property""; ""1.4. Locally finiteness and gentleness""; ""1.5. Rationally ramified self-similar sets 1""; ""1.6. Rationally ramified self-similar sets 2""; ""1.7. Examples""; ""Chapter 2. Construction of Distances""; ""2.1. Distances associated with scales""; ""2.2. Intersection type""; ""2.3. Qdistances adapted to scales""""Chapter 3. Heat Kernel and Volume Doubling Property of Measures""""3.1. Dirichlet forms on self-similar sets""; ""3.2. Heat kernel estimate""; ""3.3. P.c.f. self-similar sets""; ""3.4. Sierpinski carpets""; ""3.5. Proof of Theorem 3.2.3""; ""Appendix""; ""A. Existence and continuity of a heat kernel""; ""B. Recurrent case and resistance form""; ""C. Heat kernel estimate to the volume doubling property""; ""Bibliography""; ""Assumptions, Conditions and Properties in Parentheses""; ""List of Notations""; ""Index""; ""A""; ""C""; ""D""; ""E""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""""P""""Q""; ""R""; ""S""; ""U""; ""V""; ""W""Memoirs of the American Mathematical Society ;Volume 199, Number 932.Measure theoryFractalsSelf-similar processesMeasure theory.Fractals.Self-similar processes.515.42Kigami Jun65976MiAaPQMiAaPQMiAaPQBOOK9910811735903321Volume doubling measures and heat kernel estimates on self-similar sets3990279UNINA