Author(s)

Salvador Godoy, Karen Villa

Departamento de Fsica, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, México.

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, $g\left(x^{\prime }\right)=\pm Sgn\left(x^{\prime }\right)g\left(x^{\prime }\right)$ , 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.

Diffraction in Time, Dispersion Relations, Hilbert Transforms

Godoy, S. and Villa, K. (2024) Dispersion Relations in Diffraction in Time. Applied Mathematics, 15, 464-468. doi: 10.4236/am.2024.157028.