M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

被引：53

作者：

Brown, B. M. ^{[2
]}

Grubb, G. ^{[1
]}

Wood, I. G. ^{[3
]}

机构：

[1] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

[2] Cardiff Univ, Cardiff Sch Comp Sci, Cardiff CF24 3AA, Wales

[3] Aberystwyth Univ, Inst Math & Phys, Ceredigion SY23 3BZ, Wales

来源：

MATHEMATISCHE NACHRICHTEN | 2009年 / 282卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Closed extension; M-function; abstract boundary spaces; boundary triplets; elliptic PDEs; pseudo-differential boundary operators; essential spectrum; PARTIAL-DIFFERENTIAL OPERATORS; SYSTEMS;

D O I：

10.1002/mana.200810740

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that cannot be detected by the M-function. (C) 2009 WILEYNCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：314 / 347

页数：34

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