Natural Sciences, Mathematics, 2026
UNIQUENESS THEOREMS FOR MULTIPLE FRANKLIN SERIES
This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Submitted: 2025-02-05
© 2026 by author(s) and The Gufo Inc.
This work is licensed under Creative Commons Attribution–NonCommercial International License
(CC BY-NC 4.0).
Abstract
It is proved, that if the square partial sums σqn(x) of a multiple Franklin series converge in measure to a function f, the ratio qn+1qn is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function f.