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
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id	my-upm-ir.79204
record_format	uketd_dc
spelling	my-upm-ir.792042022-01-12T04:42:52Z Convergence problems of the eigenfunction expansions for polyharmonic operators 2018-11 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. Operator theory Eigenfunction expansions 2018-11 Thesis http://psasir.upm.edu.my/id/eprint/79204/ http://psasir.upm.edu.my/id/eprint/79204/1/IPM%202019%2010%20ir.pdf text en public doctoral Universiti Putra Malaysia Operator theory Eigenfunction expansions Ibragimov, Gafurjan
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Ibragimov, Gafurjan
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
qualification_level	Doctorate
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
granting_institution	Universiti Putra Malaysia
publishDate	2018
url	http://psasir.upm.edu.my/id/eprint/79204/1/IPM%202019%2010%20ir.pdf
_version_	1747813310325063680

Convergence problems of the eigenfunction expansions for polyharmonic operators

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