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Abstract:

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.

Registro:

Documento: Artículo
Título:On the Laplace transforms of retarded, Lorentz-invariant functions
Autor:Domínguez, A.G.; Trione, S.E.
Filiación: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
Año:1979
Volumen:31
Número:1
Página de inicio:51
Página de fin:62
DOI: http://dx.doi.org/10.1016/0001-8708(79)90019-7
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v31_n1_p51_Dominguez.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v31_n1_p51_Dominguez

Referencias:

  • Bochner, (1932) Vorlesungen uber Fouriersche Integrale, , Akad. Verlagsgesellschaft, Leipzig
  • Bateman Manuscript Project (1954) Tables of Integral Transforms, 1-2. , 2nd ed., McGraw-Hill, New York
  • Oberhettinger, (1972) Tables of Bessel Transforms, , Springer-Verlag, Berlin
  • Leray, Hyperbolic Differential Equations (1952) mimeographed lecture notes, , Institute of Advanced Study, Princeton, N.J
  • Watson, (1944) A Treatise on the Theory of Bessel Functions, , 2nd ed., Cambridge Press, London/New York
  • Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy pour l'équation des ondes (1939) Comm. Sém. Math. Univ. de Lund, 4
  • Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy (1949) Acta Math., 81, pp. 1-223
  • Schwartz, (1966) Théorie des distributions, , Hermann, Paris
  • Fremberg, A Study of Generalized Hyperbolic Potentials (1946) Thesis, , Lund
  • Gelfand, Shilov, (1964) Generalized Functions, 1. , Academic Press, New York
  • Vladimirov, (1966) Methods of the Theory of Functions of Several Complex Variables, , M.I.T. Press, Cambridge, Mass
  • Bremermann, (1965) Distributions, Complex Variables, and Fourier Transforms, , Addison-Wesley, Reading, Mass
  • Lavoine, Solutions de l'équation de Klein-Gordon (1961) Bull. Sci. Math., 85, pp. 57-72

Citas:

---------- APA ----------
Domínguez, A.G. & Trione, S.E. (1979) . On the Laplace transforms of retarded, Lorentz-invariant functions. Advances in Mathematics, 31(1), 51-62.
http://dx.doi.org/10.1016/0001-8708(79)90019-7
---------- CHICAGO ----------
Domínguez, A.G., Trione, S.E. "On the Laplace transforms of retarded, Lorentz-invariant functions" . Advances in Mathematics 31, no. 1 (1979) : 51-62.
http://dx.doi.org/10.1016/0001-8708(79)90019-7
---------- MLA ----------
Domínguez, A.G., Trione, S.E. "On the Laplace transforms of retarded, Lorentz-invariant functions" . Advances in Mathematics, vol. 31, no. 1, 1979, pp. 51-62.
http://dx.doi.org/10.1016/0001-8708(79)90019-7
---------- VANCOUVER ----------
Domínguez, A.G., Trione, S.E. On the Laplace transforms of retarded, Lorentz-invariant functions. Adv. Math. 1979;31(1):51-62.
http://dx.doi.org/10.1016/0001-8708(79)90019-7