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

被引：4
|
作者：
Kudaybergenov, K. [1 ]
Mukhamedov, F. [2 ]
机构：
[1] Karakalpak State Univ, Dept Math, Nukus 230113, Uzbekistan
[2] Int Islamic Univ Malaysia, Dept Computat & Theoret Sci, Fac Sci, POB 141, Kuantan 25710, Pahang, Malaysia
来源：
ACTA MATHEMATICA HUNGARICA | 2016年 / 149卷 / 02期
关键词：
cyclically compact operator; partial integral equation; spectral decomposition;
D O I：
10.1007/s10474-016-0619-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：297 / 305
页数：9
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