<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this work, we consider a boundary value problem for a <italic>q</italic>-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.</p>
</abstract>

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.

Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function"}

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...

Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function

Published Online: Jun 28, 2023

Page range: 1 - 18

Received: Sep 02, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0011

Keywords
Dirac operator, -calculus, boundary value problem, inverse problem, Weyl function

© 2023 Martin Bohner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function

Published Online: Jun 28, 2023

Page range: 1 - 18

Received: Sep 02, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0011

KeywordsDirac operator, -calculus, boundary value problem, inverse problem, Weyl function

© 2023 Martin Bohner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Dirac operator, -calculus, boundary value problem, inverse problem, Weyl function