On the Fourier transforms of retarded Lorentz-invariant functions
In this article we evaluate the Fourier transforms of retarded Lorentz-invariant functions (and distributions) as limits of Laplace transforms. Our method works generally for any retarded Lorentz-invariant functions φ(t) (t ε{lunate} Rn) which is, besides, a continuous function of slow growth. We gi...
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| Formato: | Artículo publishedVersion |
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1981
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v84_n1_p73_Trione_oai |
| Aporte de: |
| Sumario: | In this article we evaluate the Fourier transforms of retarded Lorentz-invariant functions (and distributions) as limits of Laplace transforms. Our method works generally for any retarded Lorentz-invariant functions φ(t) (t ε{lunate} Rn) which is, besides, a continuous function of slow growth. We give, among others, the Fourier transform of GR(t, α, m2, n) and GA(t, α, m2, n), which, in the particular case α = 1, are the characteristic functions of the volume bounded by the forward and the backward sheets of the hyperboloid u = m2 and by putting α = -k are the derivatives of k-order of the retarded and the advanced-delta on the hyperboloid u = m2. We also obtain the Fourier transform of the function W(t, α, m2, n) introduced by M. Riesz (Comm. Sem. Mat. Univ. Lund4 (1939)). We finish by evaluating the Fourier transforms of the distributional functions GR(t, α, m2, n), GA(t, α, m2, n) and W(t, α, m2, n) in their singular points. © 1981. |
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