Abstract:
The paper contains two main results. First we describe one-dimensional Franklin series converging everywhere
except possibly on a finite set to an everywhere-finite integrable function. Second we establish a class of subsets
of $[0, 1]^2$ with the following property. If a double Franklin series converges everywhere except on this set to an everywhere-finite integrable function, then it is the Fourier–Franklin series of this function. In particular, all countable
sets are in this class.
Keywords:uniqueness theorem, $U$-set, Vallée–Poussin set, Franklin system, double series.
Fulltext:
PDF file (571 kB)
