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In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation , where and are Henstock-Kurzweil integrable functions on . Results presented in this article are generalizations of the classical results for the Lebesgue integral.
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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