Open AccessOn the spectral properties of the differential operators with involution
Author(s) -
Cholpon Abdullayeva,
Begimai Turdueva,
Anvarjon Ahmedov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1988/1/012083
Subject(s) - eigenfunction , mathematics , differential operator , biharmonic equation , mathematical analysis , boundary value problem , involution (esoterism) , linear map , operator (biology) , operator theory , eigenvalues and eigenvectors , pure mathematics , physics , biochemistry , chemistry , repressor , quantum mechanics , politics , political science , transcription factor , law , gene
In this paper we deal with the problems of the eigenfunction expansions related to the differential operators with involution. The mean value formula for the eigenfunction is obtained with application of the transformation methods of the operators in the symmetric regions. The obtained formula is applied to estimate the eigenfunctions of the given differential operator in the ball. For domains with smooth boundary, the solution to these differential operator problems involves eigenfunction expansions associated with biharmonic-type operator with Navier boundary conditions.