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# Necessary and sufficient condition for solvability of a partial integral equation

### Abstract

Let $T_1: L_2(\Omega^2) \to L_2(\Omega^2)$ be a partial integral operator [4,7] with the kernel from $C(\Omega^3)$ where $\Omega=[a,b ]^ u$, $u \in N$ is fixed. In this paper we investigate solvability of the partial integral equation $f-\varkappa T_1 f=g_0$ in the space $L_2(\Omega^2)$ in the case where $\varkappa$ is a cha ac eristic number. We prove a the theorem that gives a necessary and sufficient condition for solvability of the partial integral equation $f-\varkappa T_1 f=g_0.$

### Article Information

 Title Necessary and sufficient condition for solvability of a partial integral equation Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 67-73 MathSciNet MR2502640 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

Yu. Kh. Eshkabilov
National University of Uzbekistan, Tashkent, Uzbekistan

### Citation Example

Yu. Kh. Eshkabilov, Necessary and sufficient condition for solvability of a partial integral equation, Methods Funct. Anal. Topology 15 (2009), no. 1, 67-73.

### BibTex

@article {MFAT426,
AUTHOR = {Eshkabilov, Yu. Kh.},
TITLE = {Necessary and sufficient condition for solvability of a partial integral equation},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {1},
PAGES = {67-73},
ISSN = {1029-3531},
MRNUMBER = {MR2502640},
URL = {http://mfat.imath.kiev.ua/article/?id=426},
}