Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 4Citation - Scopus: 4On Schrödinger Operators Modified by Δ Interactions(Academic Press, 2023) Akbaş, Kaya Güven; Erman, Fatih; Turgut, O. TeomanWe study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly. © 2023 Elsevier Inc.Article Citation - WoS: 1Citation - Scopus: 1Discrete Fractional Integral Operators With Binary Quadratic Forms as Phase Polynomials(Academic Press, 2019) Temur, Faruk; Sert, EzgiWe give estimates on discrete fractional integral operators along binary quadratic forms. These operators have been studied for 30 years starting with the investigations of Arkhipov and Oskolkov, but efforts have concentrated on cases where the phase polynomial is translation invariant or quasi-translation invariant. This work presents the first results for operators with neither translation invariant nor quasi-translation invariant phase polynomials. (C) 2019 Elsevier Inc. All rights reserved.