On characteristic functions of generalized resolvents generated by integral equations with operator measures

Author:

Bruk Vladislav1

Affiliation:

1. Saratov State Technical University, Saratov, Russia

Abstract

We consider a symmetric minimal relation L0 generated by an integral equation with operators measures. We describe the generalized resolvents of L0 using the characteristic function M(?) (? ? C), i.e., a function that has the property (Im?)?1ImM(?) ? 0. We obtain a necessary and sufficient condition for a holomorphic function M(?) to be a characteristic function of a generalized resolvent. We give a detailed example of finding the characteristic function.

Publisher

National Library of Serbia

Reference27 articles.

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2. A. G. Baskakov, Analysis of Linear Differential Equations by Methods of the Spectral Theory of Difference Operators and Linear Relations, Uspekhi Mat. Nauk 68 (2013), No.1, 77-128

3. Engl. transl.: Russian Mathematical Surveys 68 (2013), No.1, 69-116.

4. J. Behrndt, S. Hassi, H. Snoo, R. Wietsma, Square-Integrable Solutions and Weil functions for Singular Canonical Systems, Math. Nachr. 284 (2011), No.11-12, 1334-1384.

5. Yu. M. Berezanski, Expansions in Eigenfunctions of Selfadjoint Operators, Naukova Dumka, Kiev, 1965; Engl. transl.: Amer. Math. Soc., Providence, RI, 1968.

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