Optimal codomains for the Laplace operator and the product Laplace operator
An optimal codomain for an operator P (∂) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P (∂)S=T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the pro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/257051 |
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| _version_ | 1849683705399869440 |
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| author | Josefina Alvarez Lloyd Edgar S. Moyo |
| author_facet | Josefina Alvarez Lloyd Edgar S. Moyo |
| author_sort | Josefina Alvarez |
| collection | DOAJ |
| description | An optimal codomain for an operator P (∂) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P (∂)S=T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case. The convolution is understood in the sense of the S′-convolution. |
| format | Article |
| id | doaj-art-cf39f37962f44abe8cdf76a675ff8f27 |
| institution | DOAJ |
| issn | 0972-6802 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-cf39f37962f44abe8cdf76a675ff8f272025-08-20T03:23:43ZengWileyJournal of Function Spaces and Applications0972-68022007-01-015326928510.1155/2007/257051Optimal codomains for the Laplace operator and the product Laplace operatorJosefina Alvarez0Lloyd Edgar S. Moyo1Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USADepartment of Mathematics, Sul Ross State University, Alpine, Texas 79832, USAAn optimal codomain for an operator P (∂) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P (∂)S=T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case. The convolution is understood in the sense of the S′-convolution.http://dx.doi.org/10.1155/2007/257051 |
| spellingShingle | Josefina Alvarez Lloyd Edgar S. Moyo Optimal codomains for the Laplace operator and the product Laplace operator Journal of Function Spaces and Applications |
| title | Optimal codomains for the Laplace operator and the product Laplace operator |
| title_full | Optimal codomains for the Laplace operator and the product Laplace operator |
| title_fullStr | Optimal codomains for the Laplace operator and the product Laplace operator |
| title_full_unstemmed | Optimal codomains for the Laplace operator and the product Laplace operator |
| title_short | Optimal codomains for the Laplace operator and the product Laplace operator |
| title_sort | optimal codomains for the laplace operator and the product laplace operator |
| url | http://dx.doi.org/10.1155/2007/257051 |
| work_keys_str_mv | AT josefinaalvarez optimalcodomainsforthelaplaceoperatorandtheproductlaplaceoperator AT lloydedgarsmoyo optimalcodomainsforthelaplaceoperatorandtheproductlaplaceoperator |