On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions

被引：7

作者：

Posilicano, Andrea ^{[1
]}

机构：

[1] Univ Insubria, DiSAT Sez Matemat, Como, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 03期

关键词：

Dirichlet Laplacians; Point interactions; Self-adjoint extensions; Krein's resolvent formula; SELF-ADJOINT EXTENSIONS; PERTURBATIONS; OPERATORS;

D O I：

10.1016/j.jfa.2013.05.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By Birman and Skvortsov it is known that if Omega is a planar curvilinear polygon with n non-convex corners then the Laplace operator with domain H-2(Omega) boolean AND H-0(1)(Omega) is a closed symmetric operator with deficiency indices (n, n). Here we provide a Krein-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on Omega, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with n point interactions. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：303 / 323

页数：21

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