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# Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich

### Abstract

The main object of the paper is a Hamiltonian system $J y'-B(t)y=\lambda\Delta(t) y$ defined on an interval $[a,b)$ with the regular endpoint $a$. We define a pseudo\-spectral function of a singular system as a matrix-valued distribution function such that the generalized Fourier transform is a partial isometry with the minimally possible kernel. Moreover, we parameterize all spectral and pseudospectral functions of a given system by means of a Nevanlinna boundary parameter. The obtained results develop the results by Arov-Dym and Sakhnovich in this direction.

Key words: Hamiltonian system, spectral function, pseudospectral function, Fourier transform, $m$-function.

### Article Information

 Title Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich Source Methods Funct. Anal. Topology, Vol. 21 (2015), no. 4, 370-402 MathSciNet MR3469534 zbMATH 06630280 Milestones Received 13/02/2015; Revised 09/03/2015 Copyright The Author(s) 2015 (CC BY-SA)

### Citation Example

Vadim Mogilevskii, Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich, Methods Funct. Anal. Topology 21 (2015), no. 4, 370-402.

### BibTex

@article {MFAT784,
TITLE = {Spectral and pseudospectral  functions of  Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {4},
PAGES = {370-402},
ISSN = {1029-3531},
MRNUMBER = {MR3469534},
ZBLNUMBER = {06630280},
URL = {http://mfat.imath.kiev.ua/article/?id=784},
}

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