ON THE BASIS PROPERTY OF AN TRIGONOMETRIC FUNCTIONS SYSTEM OF THE FRANKL PROBLEM WITH A NONLOCAL PARITY CONDITION IN THE SOBOLEV SPACE W^2l p (0; π)

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 W^2l p (0; π), where W^2l p (0; π) be the set of functions f 2 W2l p (0; π), satisfying of the following conditions: f^(2k-1)(0) = 0; k = 1; 2; ..., l.