Necessary and sufficient condition for solvability of a partial integral equation - Eshkabilov, Yu. Kh. (Methods of Functional Analysis and Topology, 2009)
Let T_1: L_2(Ω^2) → L_2(Ω^2) be a partial integral operator [4,7] with the kernel from C(Ω^3) where Ω=[a,b ]^ u, u N is fixed. In this paper we investigate solvability of the partial integral equation f-T_1 f=g_0 in the space L_2(Ω^2) in the case where 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-T_1 f=g_0.