On a non-self adjoint expansion formula
This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a≤r<∞ where a>0 The transform i...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000454 |
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| _version_ | 1832567188671692800 |
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| author | D. Naylor |
| author_facet | D. Naylor |
| author_sort | D. Naylor |
| collection | DOAJ |
| description | This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a≤r<∞ where a>0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals. |
| format | Article |
| id | doaj-art-afa3effb157146f19b5e7b32e61f16fb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-afa3effb157146f19b5e7b32e61f16fb2025-02-03T01:02:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017341742710.1155/S0161171284000454On a non-self adjoint expansion formulaD. Naylor0Department of Applied Mathematics, The University of Western Ontario, London N6A 5B9, Ontario, CanadaThis paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a≤r<∞ where a>0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.http://dx.doi.org/10.1155/S0161171284000454integral transformseigenfunction expansionsBessel functions. |
| spellingShingle | D. Naylor On a non-self adjoint expansion formula International Journal of Mathematics and Mathematical Sciences integral transforms eigenfunction expansions Bessel functions. |
| title | On a non-self adjoint expansion formula |
| title_full | On a non-self adjoint expansion formula |
| title_fullStr | On a non-self adjoint expansion formula |
| title_full_unstemmed | On a non-self adjoint expansion formula |
| title_short | On a non-self adjoint expansion formula |
| title_sort | on a non self adjoint expansion formula |
| topic | integral transforms eigenfunction expansions Bessel functions. |
| url | http://dx.doi.org/10.1155/S0161171284000454 |
| work_keys_str_mv | AT dnaylor onanonselfadjointexpansionformula |