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Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya
Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya
Mathematics and Statistics Faculty Research & Creative Works
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.