Multidimensional P-adic Integrals in some Problems of Harmonic Analysis

The paper is a survey of results related to the problem of recovering the coefficients of some classical orthogonal series from their sums by generalized Fourier formulas. The method is based on reducing the coefficient problem to the one of recovering a function from its derivative with respect to an appropriate derivation basis. In the case of the multiple Vilenkin system the problem is solved by using a multidimensional P-adic integral.