Dissipative eigenvalue problems for a singular quantum Dirac system

Bilender Pasaoglu Allahverdiev; Yelda Aygar

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arXiv · 2608.19925

Dissipative eigenvalue problems for a singular quantum Dirac system

Bilender Pasaoglu Allahverdiev·Yelda Aygar

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Abstract

In this paper, dissipative singular $q$-Dirac operators are examined in Hilbert space $\mathcal{L}_{q}^{2}(q^{{\mathbb{Z}}};\mathbb{C}^{2})$, where they arise as extensions of a minimal symmetric operator in the limit-point case. We develop a selfadjoint dilation and get its incoming and outgoing spectral representations, enabling the explicit computation of the scattering matrix associated with the dilation. Furthermore, we construct a functional model for the dissipative operator and express its characteristic function in terms of the Titchmarsh-Weyl function of the corresponding selfadjoint operator. Finally, we establish results concerning the completeness of the system of eigenvectors and associated vectors for these dissipative Dirac operators.

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BibTeX RIS

Bilender Pasaoglu Allahverdiev, Yelda Aygar. 2026-08-20. Dissipative eigenvalue problems for a singular quantum Dirac system. https://arxiv.org/abs/2608.19925

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