This article demonstrates numerical recovery of functions using their Generalized Fourier Transform, implying new insights into integrability conditions.
The article addresses the integrability of the Fourier transform defined on the space of bounded variation functions vanishing at infinity. Explicit formulas for some involved integrals are shown. In particular, we recover the function from its Generalized Fourier Transform, which offers advantages for numerical approximations of the Fourier transform function. Moreover, an optimal condition for integrability in the Henstock-Kurzweil sense of the classic Fourier transform defined on the Lebesgue spaces is given. The condition represents an extension of the Heisenberg’s Uncertainty Principle beyond the traditional mathematical formalism in Quantum Mechanics.
No takes yet. Share an insight, caveat, or question.
Arredondo et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: