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)

Document Type : Original Article

Authors
Naser Abbasi 1
Evgenii Ivanovich Moiseev 2
1 Department of Mathematics, Lorestan University, Khorramabad, Iran.
2 Moscow State University, 119992, Russia
10.29252/maco.1.1.5
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`.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 1
June 2020
Pages 41-48