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has been cited by the following article:

• TITLE: Dispersion Relations in Diffraction in Time

  AUTHORS: Salvador Godoy, Karen Villa

  KEYWORDS: Diffraction in Time, Dispersion Relations, Hilbert Transforms

  JOURNAL NAME: Applied Mathematics, Vol.15 No.7, July 26, 2024

  ABSTRACT: In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g( x ′ )=±Sgn( x ′ )g( x ′ ) , 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.