Convolution algebras arising from Sturm-Liouville transforms and applications
A regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010584 |
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| _version_ | 1850165814909468672 |
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| author | Jason P. Huffman Henry E. Heatherly |
| author_facet | Jason P. Huffman Henry E. Heatherly |
| author_sort | Jason P. Huffman |
| collection | DOAJ |
| description | A regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a
generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm-Liouville problem. We give applications of these
convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations. |
| format | Article |
| id | doaj-art-e195a44a36b749ca82f4832208c10c96 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e195a44a36b749ca82f4832208c10c962025-08-20T02:21:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127422122810.1155/S0161171201010584Convolution algebras arising from Sturm-Liouville transforms and applicationsJason P. Huffman0Henry E. Heatherly1Department of Mathematics, Computing, and Information Sciences, Jacksonville State University, Jacksonville 36265, AL, USADepartment of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USAA regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm-Liouville problem. We give applications of these convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations.http://dx.doi.org/10.1155/S0161171201010584 |
| spellingShingle | Jason P. Huffman Henry E. Heatherly Convolution algebras arising from Sturm-Liouville transforms and applications International Journal of Mathematics and Mathematical Sciences |
| title | Convolution algebras arising from Sturm-Liouville transforms and applications |
| title_full | Convolution algebras arising from Sturm-Liouville transforms and applications |
| title_fullStr | Convolution algebras arising from Sturm-Liouville transforms and applications |
| title_full_unstemmed | Convolution algebras arising from Sturm-Liouville transforms and applications |
| title_short | Convolution algebras arising from Sturm-Liouville transforms and applications |
| title_sort | convolution algebras arising from sturm liouville transforms and applications |
| url | http://dx.doi.org/10.1155/S0161171201010584 |
| work_keys_str_mv | AT jasonphuffman convolutionalgebrasarisingfromsturmliouvilletransformsandapplications AT henryeheatherly convolutionalgebrasarisingfromsturmliouvilletransformsandapplications |