Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations

K. Kudaybergenov; F. Mukhamedov

doi:10.1007/s10474-016-0619-9

Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations

K. Kudaybergenov
, F. Mukhamedov

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.

Original language	English
Pages (from-to)	297-305
Number of pages	9
Journal	Acta Mathematica Hungarica
Volume	149
Issue number	2
DOIs	https://doi.org/10.1007/s10474-016-0619-9
Publication status	Published - Aug 1 2016
Externally published	Yes

Keywords

cyclically compact operator
partial integral equation
spectral decomposition

ASJC Scopus subject areas

General Mathematics

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10.1007/s10474-016-0619-9

Cite this

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abstract = "We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.",

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AU - Kudaybergenov, K.

AU - Mukhamedov, F.

PY - 2016/8/1

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N2 - We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.

AB - We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.

KW - cyclically compact operator

KW - partial integral equation

KW - spectral decomposition

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ER -

Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations

Abstract

Keywords

ASJC Scopus subject areas

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