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Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral

Salvador Sánchez-Perales; Francisco J. Mendoza-Torres — 2020

Czechoslovak Mathematical Journal

In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation $- y^{''} + q y = f$ , where $q$ and $f$ are Henstock-Kurzweil integrable functions on $[a, b]$ . Results presented in this article are generalizations of the classical results for the Lebesgue integral.

Some results about the Henstock-Kurzweil Fourier transform

Francisco J. Mendoza Torres; Juan A. Escamilla Reyna; Salvador Sánchez Perales — 2009

Mathematica Bohemica

We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.

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