Refined semiclassical asymptotics for fractional powers of the Laplace operator

被引：23

作者：

Frank, Rupert L. ^{[1
,2
]}

Geisinger, Leander ^{[1
,3
]}

机构：

[1] Princeton Univ, Dept Math, Washington Rd, Princeton, NJ 08544 USA

[2] CALTECH, Math 253 37, Pasadena, CA 91125 USA

[3] Univ Stuttgart, Dept Math, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2016年 / 712卷

关键词：

STABLE PROCESSES; HALF-LINE; INTERVAL; DOMAINS; TRACE;

D O I：

10.1515/crelle-2013-0120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a two-term formula for the sum of eigenvalues with the leading (Weyl) term given by the volume and the subleading term by the surface area. Our result is valid under very weak assumptions on the regularity of the boundary.

引用

页码：1 / 37

页数：37

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