On the Weyl function for complex Jacobi matrices

A. S. Mikhailov^abc, V. S. Mikhailov<sup>ac

a</sup> St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Saint Petersburg State University
^c St. Petersburg State University of Information Technologies, Mechanics and Optics

Abstract: We derive a new representation for the Weyl function associated with the complex Jacobi matrix in the finite and semi-infinite cases. In our approach we exploit connections to the discrete-time dynamical system associated with these matrices.

Key words and phrases: complex Jacobi matrices, Weyl function.

UDC: 517.984, 512.643.8, 517.962.22

Received: 05.10.2025