On the basis property of an trigonometric functions system of the Frankl problem with a nonlocal parity condition of the first kind in the Sobolev space `overline(W)_p^(2l) (0,pi)`

Abstract

In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal parity condition of the first kind. We analyze the completeness, the basis property, and the minimality of the eigenfunctions in the space `overline(W)_p^(2l) (0,pi)`, where `overline(W)_p^(2l) (0,pi)` be the set of functions `f in W_p^(2l) (0,pi)`, satisfying of the following conditions: `f^{(2k-1)}(0)=0, k=1,2,...,l`.