Partially integral operators with bounded kernels.

Let Ω = [ a, b] ^ν and let T be a partially integral operator defined in L ₂(Ω²) as follows: In the article, we study the solvability of the partially integral Fredholm equations f − ℵ Tf = g, where g ∈ L ₂(Ω²) is a given function and ℵ ∈ ℂ. The notion of determinant (which is a measurable function on Ω) is introduced for the operator E − ℵ T, with E is the identity operator in L ₂(Ω²). Some theorems on the spectrum of a bounded operator T are proven. [ABSTRACT FROM AUTHOR]