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Convergence problems of the eigenfunction expansions for polyharmonic operators

This research focuses on convergence and summability problems of the eigenfunctions expansions of differential operators related to polyharmonic operator in closed domain. The polyharmonic operator (-- ∆)‴,m ∈ Z+ is the elliptic operator of order 2m with domain consists of classes of infinitely diff...

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Main Author: Mohd Aslam, Siti Nor Aini
Format: Thesis
Language:English
Published: 2018
Subjects:
Operator theory
Eigenfunction expansions
Online Access:http://psasir.upm.edu.my/id/eprint/79204/1/IPM%202019%2010%20ir.pdf
http://psasir.upm.edu.my/id/eprint/79204/
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spelling my.upm.eprints.792042022-01-12T04:42:52Z http://psasir.upm.edu.my/id/eprint/79204/ Convergence problems of the eigenfunction expansions for polyharmonic operators Mohd Aslam, Siti Nor Aini This research focuses on convergence and summability problems of the eigenfunctions expansions of differential operators related to polyharmonic operator in closed domain. The polyharmonic operator (-- ∆)‴,m ∈ Z+ is the elliptic operator of order 2m with domain consists of classes of infinitely differentiable functions with compact support, which is a symmetric and nonnegative linear operator and has a self-adjoint extension. For domains with smooth boundary, the solution to these differential operator problems involves eigenfunction expansions associated with polyharmonic operator with Navier boundary conditions. Suitable estimations for spectral function of the polyharmonic operator by using the mean value formula for the eigenfunctions of the polyharmonic operator is established. These estimations enable us to show the uniformly convergence of the Riesz means of the spectral expansions related to polyharmonic operator in closed domain. The classes of differentiable functions used are Sobolev and Nikolskii classes. Subsequently, the results are applied to study the sufficient conditions for localization properties of the spectral expansions related to distributions. The conditions and principles for the localization of the Riesz means spectral expansions of distributions associated with the polyharmonic operator in closed domain are considered. 2018-11 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/79204/1/IPM%202019%2010%20ir.pdf Mohd Aslam, Siti Nor Aini (2018) Convergence problems of the eigenfunction expansions for polyharmonic operators. Doctoral thesis, Universiti Putra Malaysia. Operator theory Eigenfunction expansions
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
topic Operator theory
Eigenfunction expansions
spellingShingle Operator theory
Eigenfunction expansions
Mohd Aslam, Siti Nor Aini
Convergence problems of the eigenfunction expansions for polyharmonic operators
description This research focuses on convergence and summability problems of the eigenfunctions expansions of differential operators related to polyharmonic operator in closed domain. The polyharmonic operator (-- ∆)‴,m ∈ Z+ is the elliptic operator of order 2m with domain consists of classes of infinitely differentiable functions with compact support, which is a symmetric and nonnegative linear operator and has a self-adjoint extension. For domains with smooth boundary, the solution to these differential operator problems involves eigenfunction expansions associated with polyharmonic operator with Navier boundary conditions. Suitable estimations for spectral function of the polyharmonic operator by using the mean value formula for the eigenfunctions of the polyharmonic operator is established. These estimations enable us to show the uniformly convergence of the Riesz means of the spectral expansions related to polyharmonic operator in closed domain. The classes of differentiable functions used are Sobolev and Nikolskii classes. Subsequently, the results are applied to study the sufficient conditions for localization properties of the spectral expansions related to distributions. The conditions and principles for the localization of the Riesz means spectral expansions of distributions associated with the polyharmonic operator in closed domain are considered.
format Thesis
author Mohd Aslam, Siti Nor Aini
author_facet Mohd Aslam, Siti Nor Aini
author_sort Mohd Aslam, Siti Nor Aini
title Convergence problems of the eigenfunction expansions for polyharmonic operators
title_short Convergence problems of the eigenfunction expansions for polyharmonic operators
title_full Convergence problems of the eigenfunction expansions for polyharmonic operators
title_fullStr Convergence problems of the eigenfunction expansions for polyharmonic operators
title_full_unstemmed Convergence problems of the eigenfunction expansions for polyharmonic operators
title_sort convergence problems of the eigenfunction expansions for polyharmonic operators
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/79204/1/IPM%202019%2010%20ir.pdf
http://psasir.upm.edu.my/id/eprint/79204/
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score 13.211869

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