On the Laplace transforms of retarded,Lorentz-invariant functions |
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Authors: | Alberto González Domínguez Susana Elena Trione |
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Affiliation: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina;Instituto Argentino de Matemática, Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina |
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Abstract: | Let ø(t) (t ∈ n) 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) ∈ . 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. |
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