In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.
M. Bohner and A. Çetinkaya, "Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function," Tatra Mountains Mathematical Publications, vol. 84, no. 2, pp. 1 - 18, Sciendo, Jun 2023.
The definitive version is available at https://doi.org/10.2478/tmmp-2023-0011
Mathematics and Statistics
Keywords and Phrases
boundary value problem; Dirac operator; inverse problem; q-calculus; Weyl function
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2023