We study the recovery of continuous functions from Fourier coefficients with respect to certain given orthonormal systems, blurred by noise. For deterministic noise this is a classical ill–posed problem. Emphasis is laid on a priori smoothness assumptions on the solution, which allows to apply regularization to reach the best possible accuracy. Results are… (More)

Encyclopedia of Mathematics & its Appl. Cambridge…

1991

Probability in Banach spaces

Michel Ledoux, Michel Talagrand

Isoperimetry and processes

1991

Orthogonal series

B. S. Kashin, A. A. Saakyan

Transl. from the Russian by Ralph P. Boas. Transl…

1989

Theory and methods of solving ill-posed problems

O. A. Liskovets

In Mathematical analysis, Vol. 20, pages 116–178…

1982

Estimation of the regularization method for the problem of the summability of the Fourier series

B. Aliev

Dokl. Akad. Nauk Tadzhik. SSR, 21(4):3–6,

1978

Solutions of ill-posed problems

Andrey N. Tikhonov, Vasiliy Y. Arsenin

New York,

1977

An application of the interpolation of linear operators to questions of the convergence of series of Fourier coefficients with respect to classical orthogonal polynomials