Counting function asymptotics and the weak Weyl-Berry conjecture for connected domains with fractal boundaries

被引：0

作者：

Chen Hua

Brian D. Sleeman

机构：

[1] Wuhan University,Department of Mathematics

[2] University of Leeds,School of Mathematics

来源：

Acta Mathematica Sinica | 1998年 / 14卷 / 2期

关键词：

Connected fractal domain; Counting function; Wely-Berry conjecture; 34L20; 35P15; 35P20; O175.25; O175.9;

D O I：

10.1007/BF02560212

中图分类号：

学科分类号：

摘要：

In this paper, we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture. We prove, for some special connected fractal domains, the sharp estimate for second term of counting function asymptotics, which implies that the weak form of the Weyl-Berry conjecture holds for the case. Finally, we also study a naturally connected fractal domain, and we prove, in this case, the weak Weyl-Berry conjecture holds as well.

引用

页码：261 / 276

页数：15

共 23 条

[1] Counting function asymptotics and the weak Weyl-Berry conjecture for connected domains with fractal boundaries
Chen, H
Sleeman, BD
[J]. ACTA MATHEMATICA SINICA-NEW SERIES, 1998, 14 (02): : 261 - 276
[2] Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries
Chen Hua Department of MathematicsWuhan UniversityWuhan ChinaEmailchenhuawhueducnBrian DSleeman School of MathematicsUniversity of LeedsLeeds LS JTEnglandUKEmailbdsamstaleedsacuk
[J]. Acta Mathematica Sinica(New Series)., 1998, 14 (02) - 276
[3] Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries
Chen Hua (Department of Mathematics
[J]. Acta Mathematica Sinica,English Series, 1998, (02) : 261 - 276
[4] On a pair of non-isometric isospectral domains with fractal boundaries and the Weyl-Berry conjecture
Sleeman, BD
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[5] ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE
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[J]. Chinese Annals of Mathematics,Series B, 1998, (01) : 9 - 20
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