Volume doubling measures and heat kernel estimates on self-similar sets. Memoirs of the American Mathematical Society; no. 932.

Kigami, Jun:

ISBN 10: 0821842927 / ISBN 13: 9780821842928

Published by Providence R.I, American Mathematical Society, 2009

About this Item

94 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04923 9780821842928 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2491166

Bibliographic Details

• Title: Volume doubling measures and heat kernel estimates on self-similar sets. Memoirs of the American Mathematical Society; no. 932.
• Publisher: Providence R.I, American Mathematical Society
• Publication Date: 2009
• Language: English
• ISBN 10: 0821842927
• ISBN 13: 9780821842928
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

This paper studies the following three problems. 1. When does a measure on a self-similar set have the volume doubling property with respect to a given distance? 2. Is there any distance on a self-similar set under which the contraction mappings have the prescribed values of contractions ratios? 3. When does a heat kernel on a self-similar set associated with a self-similar Dirichlet form satisfy the Li-Yau type sub-Gaussian diagonal estimate? These three problems turn out to be closely related. 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 and gives complete solutions of the above three problems for this class. In particular, the volume doubling property is shown to be equivalent to the upper Li-Yau type sub-Gaussian diagonal estimate of a heat kernel.