Uniqueness theorems for Franklin series converging to integrable functions

Abstract

The following results are proved: a) if a Franklin series converges everywhere to a finite integrable function, then it is the Fourier- Franklin series of this function; b) if a Franklin series converges to a finite integrable function everywhere except possibly at points in some countable set and if all its coefficients satisfy a certain necessary condition, then it is the Fourier-Franklin series of this function. Bibliography: 16 titles.