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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Online Access: | http://dx.doi.org/10.1155/S0161171284000247 |
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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 |
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1725822430340972544 |