Finite-Dimensional Perturbations of Integral Operators with Kernels Discontinuous on the Diagonals
Copyright policy )Finite-Dimensional Perturbations of Integral Operators with Kernels Discontinuous on the Diagonals
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.
- Saratov State University Russian Federation
Integral operators, series expansions in eigenfunctions, Fredholm resolvent, integro-differential operator, integral operator, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, equiconvergence of series expansions, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
Integral operators, series expansions in eigenfunctions, Fredholm resolvent, integro-differential operator, integral operator, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, equiconvergence of series expansions, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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