Аннотация:We discuss various ways for solution of the problem of recovering the coefficients of point-wise convergent series with respect to the sequence of characters of compact group. Two typical (in a certain way opposite) cases of compact abelian groups are the one-dimensional torus, on one side, and the family of so-called zero-dimensional groups (Cantor dyadic group or group of $p$-adic integers), on the other side. For these groups a complete solution is found by constructing generalized integrals to be used in the generalized Fourier formulae.
