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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1979
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v31_n1_p51_Dominguez http://hdl.handle.net/20.500.12110/paper_00018708_v31_n1_p51_Dominguez |
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paper:paper_00018708_v31_n1_p51_Dominguez2023-06-08T14:21:50Z On the Laplace transforms of retarded, Lorentz-invariant functions Trione, Susana Elena 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. 1979 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v31_n1_p51_Dominguez 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 |
| collection |
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. |
| author |
Trione, Susana Elena |
| spellingShingle |
Trione, Susana Elena On the Laplace transforms of retarded, Lorentz-invariant functions |
| author_facet |
Trione, Susana Elena |
| author_sort |
Trione, Susana Elena |
| 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 |
| publishDate |
1979 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v31_n1_p51_Dominguez http://hdl.handle.net/20.500.12110/paper_00018708_v31_n1_p51_Dominguez |
| work_keys_str_mv |
AT trionesusanaelena onthelaplacetransformsofretardedlorentzinvariantfunctions |
| _version_ |
1768544527356788736 |