8 citations · 46 across the 25 of their papers we have counts for
6 papers · 1 filter
On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study
Steve Clark, Fritz Gesztesy
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing…
Evans Functions, Jost Functions, and Fredholm Determinants
Fritz Gesztesy, Yuri Latushkin, Konstantin A. Makarov
The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first…
When is a non-self-adjoint Hill operator a spectral operator of scalar type?
Fritz Gesztesy, Vadim Tkachenko
We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H=-d^2/dx^2+V in L^2(R) to be a spectral operator of scalar type. The…
On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients
Vladimir Batchenko, Fritz Gesztesy
We characterize the spectrum of one-dimensional Jacobi operators H=aS^{+}+a^{-}S^{-}+b in l^{2}(\Z) with quasi-periodic complex-valued algebro-geometric coefficients (which satisfy…
A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle
Fritz Gesztesy, Maxim Zinchenko
We prove a general Borg-type result for reflectionless unitary Cantero-Moral-Velazquez (CMV) operators U associated with orthogonal polynomials on the unit circle. The spectrum of…
Weyl-Titchmarsh Theory for CMV Operators Associated with Orthogonal Polynomials on the Unit Circle
Fritz Gesztesy, Maxim Zinchenko
We provide a detailed treatment of Weyl-Titchmarsh theory for half-lattice and full-lattice Cantero-Moral-Velazquez (CMV) operators and discuss their systems of orthonormal Laurent…