On a non-self adjoint eigenfunction expansion

This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1)(kr), in which r varies over a truncated infinite interval a≤r<∞, where a>0 and the parameter k is complex. Th...

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Bibliographic Details
Main Author:	D. Naylor
Format:	Article
Language:	English
Published:	Hindawi Limited 1984-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	integral transforms eigenfunction expansion Bessel functions Hankel function.
Online Access:	http://dx.doi.org/10.1155/S0161171284000247

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record_format	Article
spelling	doaj-559dc5d06a444f39a4158289272749ca2020-11-24T22:06:42ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017223524810.1155/S0161171284000247On a non-self adjoint eigenfunction expansionD. Naylor0Department of Applied Mathematics, The University of Western Ontario, Ontario, London N6A 5B9, CanadaThis paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1)(kr), in which r varies over a truncated infinite interval a≤r<∞, where a>0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.http://dx.doi.org/10.1155/S0161171284000247integral transformseigenfunction expansionBessel functionsHankel function.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	D. Naylor
spellingShingle	D. Naylor On a non-self adjoint eigenfunction expansion International Journal of Mathematics and Mathematical Sciences integral transforms eigenfunction expansion Bessel functions Hankel function.
author_facet	D. Naylor
author_sort	D. Naylor
title	On a non-self adjoint eigenfunction expansion
title_short	On a non-self adjoint eigenfunction expansion
title_full	On a non-self adjoint eigenfunction expansion
title_fullStr	On a non-self adjoint eigenfunction expansion
title_full_unstemmed	On a non-self adjoint eigenfunction expansion
title_sort	on a non-self adjoint eigenfunction expansion
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1984-01-01
description	This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1)(kr), in which r varies over a truncated infinite interval a≤r<∞, where a>0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.
topic	integral transforms eigenfunction expansion Bessel functions Hankel function.
url	http://dx.doi.org/10.1155/S0161171284000247
work_keys_str_mv	AT dnaylor onanonselfadjointeigenfunctionexpansion
_version_	1725822430340972544

On a non-self adjoint eigenfunction expansion

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