Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

теорема равносходимости

Equiconvergence Theorem for Integral Operator with Involution

In the paper, the integral operator with kernel having discontinuities of the first kind at the lines t = x and t = 1 − x is studied. The equiconvergence of Fourier expansions for arbitrary integrable function f(x) in eigenfunctions and associated functions of the considered operator and expansions of linear combination of functions f(x) and f(1 − x) in trigonometric system is proved. The equiconvergence is studied using the method based on integration of the resolvent using spectral value. Methods, developed by A. P.