A Blaschke-type condition and its application to complex Jacobi matrices
A. Borichev, L. Golinskii, S. Kupin
TL;DR
This paper establishes Blaschke-type conditions on zeros of analytic functions with exponential growth, and applies these results to derive inequalities for eigenvalues of complex Jacobi matrices.
Contribution
It introduces new Blaschke-type conditions for analytic functions with exponential boundary growth and applies them to complex Jacobi matrices.
Findings
Derived Blaschke-type zero conditions for exponential growth functions
Proved Lieb-Thirring-type inequalities for complex Jacobi matrix eigenvalues
Extended classical results to complex and non-self-adjoint settings
Abstract
We obtain a Blaschke-type necessary conditions on zeros of analytic functions on the unit disk with different types of exponential growth at the boundary. These conditions are used to prove Lieb-Thirring-type inequalities for the eigenvalues of complex Jacobi matrices.
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