Eigenvalues of the fractional Laplace operator in the interval

被引：102

作者：

Kwasnicki, Mateusz ^{[1
,2
]}

机构：

[1] Polish Acad Sci, Inst Math, PL-00976 Warsaw, Poland

[2] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 05期

关键词：

Fractional Laplacian; Stable process; Eigenvalues; Interval; SUBORDINATE PROCESSES; CAUCHY PROCESS; CONTINUITY;

D O I：

10.1016/j.jfa.2011.12.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two-term Weyl-type asymptotic law for the eigenvalues of the one-dimensional fractional Laplace operator (-Delta)(alpha/2) (alpha is an element of (0, 2)) in the interval (-1, 1) is given: the n-th eigenvalue is equal to (n pi/2 - (2 - alpha)pi/8)(alpha) O(1/n). Simplicity of eigenvalues is proved for alpha is an element of [1, 2). L-2 and L-infinity properties of eigenfunctions are studied. We also give precise numerical bounds for the first few eigenvalues. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2379 / 2402

页数：24

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