On the Laplace transforms of retarded, Lorentz-invariant functions
Let ø(t) (t ∈ Rn) be a retarded, Lorentz-invariant function which satisfies, in addition, condition (c). We call "R" the family of such functions. Let f(z) be the Laplace transform of ø(t) ∈ R. We prove (Theorem 1) that f(z) can be expressed as a K-transform (formula (I, 2; 1)). We apply t...
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todo:paper_00018708_v31_n1_p51_Dominguez2023-10-03T13:52:22Z On the Laplace transforms of retarded, Lorentz-invariant functions Domínguez, A.G. Trione, S.E. Let ø(t) (t ∈ Rn) be a retarded, Lorentz-invariant function which satisfies, in addition, condition (c). We call "R" the family of such functions. Let f(z) be the Laplace transform of ø(t) ∈ R. We prove (Theorem 1) that f(z) can be expressed as a K-transform (formula (I, 2; 1)). We apply this formula to evaluate several Laplace transforms. We show that it affords simple proofs of important known results. Formula (I, 2; 1) is an effective complement to L. Schwartz' method of evaluating Fourier transforms via Laplace transforms ("Théorie des distributions," p. 264, Hermann, Paris, 1966). We think this is the most useful application of our formula. © 1979. Fil:Trione, S.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00018708_v31_n1_p51_Dominguez |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Let ø(t) (t ∈ Rn) be a retarded, Lorentz-invariant function which satisfies, in addition, condition (c). We call "R" the family of such functions. Let f(z) be the Laplace transform of ø(t) ∈ R. We prove (Theorem 1) that f(z) can be expressed as a K-transform (formula (I, 2; 1)). We apply this formula to evaluate several Laplace transforms. We show that it affords simple proofs of important known results. Formula (I, 2; 1) is an effective complement to L. Schwartz' method of evaluating Fourier transforms via Laplace transforms ("Théorie des distributions," p. 264, Hermann, Paris, 1966). We think this is the most useful application of our formula. © 1979. |
| format |
JOUR |
| author |
Domínguez, A.G. Trione, S.E. |
| spellingShingle |
Domínguez, A.G. Trione, S.E. On the Laplace transforms of retarded, Lorentz-invariant functions |
| author_facet |
Domínguez, A.G. Trione, S.E. |
| author_sort |
Domínguez, A.G. |
| title |
On the Laplace transforms of retarded, Lorentz-invariant functions |
| title_short |
On the Laplace transforms of retarded, Lorentz-invariant functions |
| title_full |
On the Laplace transforms of retarded, Lorentz-invariant functions |
| title_fullStr |
On the Laplace transforms of retarded, Lorentz-invariant functions |
| title_full_unstemmed |
On the Laplace transforms of retarded, Lorentz-invariant functions |
| title_sort |
on the laplace transforms of retarded, lorentz-invariant functions |
| url |
http://hdl.handle.net/20.500.12110/paper_00018708_v31_n1_p51_Dominguez |
| work_keys_str_mv |
AT dominguezag onthelaplacetransformsofretardedlorentzinvariantfunctions AT trionese onthelaplacetransformsofretardedlorentzinvariantfunctions |
| _version_ |
1807314397387816960 |