On Eigenfunctions and Eigenvalues of a Nonlocal Laplace Operator with Multiple Involution

被引：9
作者：
Turmetov, Batirkhan [1 ]
Karachik, Valery [2 ]
机构：
[1] Khoja Akhmet Yassawi Int Kazakh Turkish Univ, Dept Math, Turkistan 161200, Kazakhstan
[2] South Ural State Univ NRU, Dept Math Anal, Chelyabinsk 454080, Russia
来源：
SYMMETRY-BASEL | 2021年 / 13卷 / 10期
关键词：
nonlocal Laplace operator; multiple involution; Dirichlet problem; eigenfunctions; eigenvalues; BOUNDARY-VALUE-PROBLEMS; 2ND-ORDER DIFFERENTIAL-EQUATION; SPECTRAL-ANALYSIS; INVERSE PROBLEM; ROOT FUNCTIONS; BASIS PROPERTY; SYSTEM; SOLVABILITY;
D O I：
10.3390/sym13101781
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We study the eigenfunctions and eigenvalues of the boundary value problem for the nonlocal Laplace equation with multiple involution. An explicit form of the eigenfunctions and eigenvalues for the unit ball are obtained. A theorem on the completeness of the eigenfunctions of the problem under consideration is proved.
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页数：20
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