Abstract:
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=∫10A(x,t)f(t)dt and to integrodifferential operators of the form
y(n)+αy+∫10N(x,t)[y(n)(t)+αy(t)]dt,Uj(y)=∫10y(t)φj(t)dt(j=1,…,n),
where α is a complex number and Uj(y) are linear forms in y(s)(0) and y(s)(1)(s=0,1,…,n−1).
Bibliography: 23 titles.
\Bibitem{Khr81}
\by A.~P.~Khromov
\paper Equiconvergence theorems for integrodifferential and integral operators
\jour Math. USSR-Sb.
\yr 1982
\vol 42
\issue 3
\pages 331--355
\mathnet{http://mi.mathnet.ru/eng/sm2330}
\crossref{https://doi.org/10.1070/SM1982v042n03ABEH002257}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=610204}
\zmath{https://zbmath.org/?q=an:0488.45016}
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https://doi.org/10.1070/SM1982v042n03ABEH002257
https://www.mathnet.ru/eng/sm/v156/i3/p378
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