Finite-dimensional perturbations of integral operators with kernels discontinuous on the diagonals (Q1578459)

The simplest integral operator \(A_0\) whose kernel is discontinuous on the diagonal is considered. In addition, \(B\) is a finite-dimensional operator. The author derives simple sufficient conditions that provide equiconvergence of spectral expansions of \(A_0\) and \(A=A_0+B\) in space \(L^1[0,1]\). In addition, the invertibility conditions for \(A\) are derived and the inverse operator \(A^{-1}\) is defined. The inverse operator is an integro-differential one. Equiconvergence of series expansions in eigenfunctions and in ordinary trigonometric functions is studied.