A Krein-like formula for singular perturbations of self-adjoint operators and applications

被引:102
作者
Posilicano, A [1 ]
机构
[1] Univ Insubria, Dipartimento Sci, I-22100 Como, Italy
关键词
D O I
10.1006/jfan.2000.3730
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a self-adjoint operator A:D(A) subset of or equal to H --> H and a continuous linear operator tau: D(A) --> X with Range tau ' boolean AND H ' = {0}, H a Banach space, we explicitly construct a family A(Theta)(tau) of self-adjoint operators such that any A(Theta)(tau) coincides with the original A on the kernel of tau. Such a family is obtained by giving a Krein-like formula where the role of the deficiency spaces is played by the dual pair (X, X '); the parameter Theta belongs to the space of symmetric operators from X ' to X. When X = C one recovers the "H-2-construction" of Kiselev and Simon and so, to some extent, our results can be regarded as an extension of it to the infinite rank case. Considering the situation in which H = L-2(R-n) and tau is the trace (restriction) operator along some null subset, we give various applications to singular perturbations of non necessarily elliptic pseudo-differential operators, thus unifying and extending previously known results. (C) 2001 Academic Press.
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页码:109 / 147
页数:39
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