EXACT SPECTRAL ASYMPTOTICS ON THE SIERPINSKI GASKET

被引：5

作者：

Strichartz, Robert S. ^{[1
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 05期

基金：

美国国家科学基金会;

关键词：

Sierpinski gasket; Laplacians on fractals; spectral asymptotics; SELF-SIMILAR SETS; FRACTALS; LAPLACIANS;

D O I：

10.1090/S0002-9939-2011-11309-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the ways that analysis on fractals is more complicated than analysis on manifolds is that the asymptotic behavior of the spectral counting function N(t) has a power law modulated by a nonconstant multiplicatively periodic function. Nevertheless, we show that for the Sierpinski gasket it is possible to write an exact formula, with no remainder term, valid for almost every t. This is a stronger result than is valid on manifolds.

引用

页码：1749 / 1755

页数：7

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