%0 Journal Article
%T Dispersion Relations in Diffraction in Time
%A Salvador Godoy
%A Karen Villa
%J Applied Mathematics
%P 464-468
%@ 2152-7393
%D 2024
%I Scientific Research Publishing
%R 10.4236/am.2024.157028
%X In agreement with Titchmarsh&#8217;s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.
%K Diffraction in Time
%K Dispersion Relations
%K Hilbert Transforms
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=134833