An addendum to Krein's formula
type: Item
instance of: scholarly article
title: An addendum to Krein's formula
zbMATH Open document ID: 0922.47006
author: K. A. Makarov
author: Eduard Tsekanovskii
author: Fritz Gesztesy
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/funct-an/9711003
review text: Some former results of Sh. N. Saakjan concerning Krein's formula for the resolvent difference of two selfadjoint extensions \(A_1\) and \(A_2\) of a densely defined closed symmetric operator \(\dot A\) with equal defect numbers are discussed and supplemented. To each selfadjoint extension \(A\) of \(\dot A\) and a subspace \(N\subset N_+= \text{ker}(\dot A^*- i)\) the Weyl-Titchmarsh operator-valued function \(M_{A,N}(z)\), \(z\in\rho(A)\), is corresponding. The linear fractional transformation relating the Weyl-Titchmarsh operators \(M_{A_1,N_+}\) and \(M_{A_2,N_+}\) is derived.
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 34B20
zbMATH DE Number: 1218621
zbMATH Keywords: Krein's formula
zbMATH Keywords: resolvent difference of two selfadjoint extensions
zbMATH Keywords: densely defined closed symmetric operator
zbMATH Keywords: Weyl-Titchmarsh operator-valued function
zbMATH Keywords: fractional transformation
MaRDI profile type: Publication
OpenAlex ID: W2078774044
arXiv ID: funct-an/9711003
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DOI: 10.1006/JMAA.1998.5948
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description: scientific article