TY - JOUR JF - lu-maco JO - MACO VL - 1 IS - 1 PY - 2020 Y1 - 2020/6/01 TI - On the Basis Property of an Trigonometric Functions System of The Frankl Problem With a Non-Local Parity Condition of the First Kind in the Sobolev Space `overline(W)_p^(2l) (0,pi)` TT - N2 - 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`. SP - 41 EP - 48 AU - Abbasi, Naser AU - Moiseev, Evgenii Ivanovich AD - Lorestan University KW - Frankl problem KW - Lebesgue integral KW - Holder inequality KW - Bessel equation KW - Sobolev space UR - http://maco.lu.ac.ir/article-1-43-en.html DO - 10.29252/maco.1.1.5 ER -