Nonharmonic analysis of boundary value problems

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Title: Nonharmonic analysis of boundary value problems
Authors: Ruzhansky, M
Tokmagambetov, N
Item Type: Journal Article
Abstract: In this paper, we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements of a non-self-adjoint distribution theory and the corresponding biorthogonal Fourier analysis. There are no assumptions on the regularity of the boundary which is allowed to have arbitrary singularities. We give applications of the developed analysis to obtain a priori estimates for solutions of boundary value problems that are elliptic within the constructed calculus.
Issue Date: 2-Sep-2015
Date of Acceptance: 23-Jul-2015
URI: http://hdl.handle.net/10044/1/25373
DOI: https://dx.doi.org/10.1093/imrn/rnv243
ISSN: 1687-0247
Publisher: Oxford University Press (OUP)
Start Page: 3548
End Page: 3615
Journal / Book Title: International Mathematics Research Notices
Volume: 2016
Issue: 12
Copyright Statement: © The Author(s) 2015. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: General Mathematics
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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