Inverse Spectral Problem for a Singular Bessel-Type Sturm–Liouville Operator on a Finite Interval

Rakib Efendiev

Abstract


This paper studies an inverse spectral problem for a singular Bessel-type Sturm–Liouville operator on a finite interval with a complex periodic potential and Robin boundary condition. A regular solution near the singular endpoint is constructed, and Jost-type solutions are introduced to analyze the spectral properties of the non-self-adjoint operator. The resolvent is constructed explicitly, and it is shown that the spectrum consists of isolated eigenvalues of finite multiplicity. The main result establishes that the spectral data uniquely determine the potential, and a constructive reconstruction procedure is provided, together with an illustrative example.

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References


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DOI: https://doi.org/10.52846/ami.v53i1.2358