Volume doubling measures and heat kernel estimates on self-similar sets / Jun Kigami.

Format:

Book

Author/Creator:

Kigami, Jun, author.

Series:

Memoirs of the American Mathematical Society ; Volume 199, Number 932.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 199, Number 932

Language:

English

Subjects (All):

Measure theory.

Fractals.

Self-similar processes.

Physical Description:

1 online resource (110 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2009.

Language Note:

English

Summary:

This paper studies three closely related problems in the field of self-similar sets. The author introduces a new class of self-similar set called rationally ramified self-similar sets containing both the Sierpinski gasket and the (higher dimensional) Sierpinski carpet, giving complete solutions to the three problems.

Contents:

""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""

Notes:

"Volume 199, Number 932 (third of 6 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0538-5