Equiconvergence theorems for integrodifferential and integral operators

A. P. Khromov

Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 331-355

Résumé

The well-known results of Steklov, Tamarkin, and Stone on the equiconvergence of Fourier expansions in eigenfunctions and associated functions of differential operators and in a trigonometrical system for arbitrary functions from $L[0,1]$ are carried over to integral operators $Af=\int^1_0A(x, t)f(t)\,dt$ and to integrodifferential operators of the form $$ y^{(n)}+\alpha y+\int^1_0N(x, t)[y^{(n)}(t)+\alpha y(t)]\,dt, \qquad U_j(y)=\int^1_0y(t)\varphi_j(t)\,dt\quad(j=1,\dots,n), $$ where $\alpha$ is a complex number and $U_j(y)$ are linear forms in $y^{(s)}(0)$ and $y^{(s)}(1)$ $(s=0,1,\dots,n-1)$. Bibliography: 23 titles.