A Krein-Like Formula for Singular Perturbations of Self-Adjoint Operators and Applications

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dc.creatorPosilicano, Andrea
dc.date2000-05-09
dc.date2000-12-14
dc.date.accessioned2026-07-07T04:35:07Z
dc.date.available2026-07-07T04:35:07Z
dc.descriptionGiven a self-adjoint operator $A:D(A)\subseteq\calH\to\calH$ and a continuous linear operator $τ:D(A)\to\X$ with Range$ τ'\cap\calH' ={0}$, $\X$ a Banach space, we explicitly construct a family $A^τ_Θ$ of self-adjoint operators such that any $A^τ_Θ$ coincides with the original $A$ on the kernel of $τ$. Such a family is obtained by giving a Kre\uın-like formula where the role of the deficiency spaces is played by the dual pair $(\X,\X')$; the parameter $Θ$ belongs to the space of symmetric operators from $\X'$ to $\X$. When $\X=\C$ one recovers the ``$\calH_{-2}$ -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 $\calH=L^2(\RE^n)$ and $τ$ 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.
dc.descriptionProposition 2.1 revised. Remarks 2.15 and 2.16 added. 38 pages. To appear in Journal of Functional Analysis
dc.identifierhttps://arxiv.org/abs/math/0005082
dc.identifierhttp://arxiv.org/abs/math/0005082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59152
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.titleA Krein-Like Formula for Singular Perturbations of Self-Adjoint Operators and Applications
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