On the basis property of a two-part trigonometric series

Abstract

Conditions are presented under which two-part trigonometric systems arising in mixed type equations form a Riesz basis in the space of Lebesgue square integrable functions. For such systems, biorthogonal systems can be obtained in explicit form. As a result, an integral representation of the solution to the Frankl problem in a special domain can be found. The results are extended to two-part systems of broader functions.