A multidimensional analogue of the A. N. Tikhonov's Theorem on calculating values of a function with respect to approximately given Fourier coefficients (Q2658367)

The notion of correctness for the formulation of mathematical physics problems was formulated at the beginning of the last century by the famous French mathematician \textit{J. Hadamard} [Lectures on Cauchy's problem in linear partial differential equations, New York: Dover Publications V, 316 p. (1952; Zbl 0049.34805)]. A mathematical physics problem is said to be correctly formulated if its solution exists, it is unique and depends continuously on the data of the problem. In recent years, it has been established that many phenomena of physics and modern technology, the mathematical description of which is associated with incorrect problems, is no longer a set of phenomena connected with problems that are correct in the classical sense. The first principles of approach to the formulation of incorrect problems, natural from the point of view of applications, were expressed by \textit{A. N. Tikhonov} [C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 39, 176--179 (1943; Zbl 0061.23308)]. As an analog of Tikhonov's theorem, the problem of reconstruction of the value of a function of several variables from the approximate values of the Fourier coefficients of a function at a given fixed point with a small error is studied in this paper.