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)`

Abbasi, Naser; Moiseev, Evgenii Ivanovich

doi:10.29252/maco.1.1.5

Volume 1, Issue 1 (6-2020) MACO 2020, 1(1): 41-48 | Back to browse issues page

‎ 10.29252/maco.1.1.5

‎ 20.1001.1.27170624.2020.1.1.5.3

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Abbasi N, Moiseev E I.

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)`

. MACO 2020; 1 (1) :41-48
URL: http://maco.lu.ac.ir/article-1-43-en.html

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)`

Naser Abbasi ^*

, Evgenii Ivanovich Moiseev

Abstract: (2098 Views)

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: Frankl problem, Lebesgue integral, Holder inequality, Bessel equation, Sobolev space

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Type of Study: Research Article |
Published: 2020/06/16

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