60 citations · 414 across the 46 of their papers we have counts for
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Analysis of the Singular Spectrum for General Perturbations
Constanze Liaw, Eero Saksman, Sergei Treil
We investigate the behavior of the singular spectrum of self-adjoint operators under families of Hermitian perturbations, even non-compact ones. Under mild assumptions we have the…
Spectral Properties of Singular Sturm-Liouville Operators via Boundary Triples and Perturbation Theory
Dale Frymark, Constanze Liaw
We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary…
Spectral Measures for Derivative Powers via Matrix-Valued Clark Theory
Michael Bush, Constanze Liaw, Robert T. W. Martin
The theory of finite-rank perturbations allows for the determination of spectral information for broad classes of operators using the tools of analytic function theory. In this wor…
Singular Boundary Conditions for Sturm--Liouville Operators via Perturbation Theory
Michael Bush, Dale Frymark, Constanze Liaw
We show that all self-adjoint extensions of semi-bounded Sturm--Liouville operators with general limit-circle endpoint(s) can be obtained via an additive singular form bounded self…
Spectral Analysis, Model Theory and Applications of Finite-Rank Perturbations
Dale Frymark, Constanze Liaw
This survey focuses on two main types of finite-rank perturbations: self-adjoint and unitary. We describe both classical and more recent spectral results. We pay special attention…
Spectral Analysis of Iterated Rank-One Perturbations
Dale Frymark, Constanze Liaw
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled ra…
Matrix Measures and Finite Rank Perturbations of Self-adjoint Operators
Constanze Liaw, Sergei Treil
Matrix-valued measures provide a natural language for the theory of finite rank perturbations. In this paper we use this language to prove some new perturbation theoretic results.…
A New Class of Exceptional Orthogonal Polynomials: The Type III -Laguerre Polynomials And The Spectral Analysis of Three Types of Exceptional Laguerre Polynomials
Constanze Liaw, Lance L. Littlejohn, Robert Milson +1
The Bochner Classification Theorem (1929) characterizes the polynomial sequences $\p_{n}\}_{n=0}^{\infty}$, with that simultaneously form a complete set of ei…
Rank one and finite rank perturbations - survey and open problems
Constanze Liaw
We survey the relationships of rank one self-adjoint and unitary perturbations as well as finite rank unitary perturbations with various branches of analysis and mathematical physi…