Uniqueness for an inverse quantum-Dirac problem with given Weyl function

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.