60 citations · 414 across the 46 of their papers we have counts for
47 papers
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…
Pairs of Clark Unitary Operators on the Bidisk and their Taylor Joint Spectra
Palak Arora, Kelly Bickel, Constanze Liaw +1
We develop a Clark theory for commuting compressed shift operators on model spaces associated with inner functions on the bidisk, which exhibits both similarities and mar…
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…
Fractional Laplacian Spectral Approach to Turbulence in a Dusty Plasma Monolayer
Evdokiya G Kostadinova, Rahul Banka, Joshua L Padgett +3
This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous form…
Perspectives on General Left-Definite Theory
Dale Frymark, Constanze Liaw
In 2002, Littlejohn and Wellman developed a celebrated general left-definite theory for semi-bounded self-adjoint operators with many applications to differential operators. The th…
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…
Preservation of absolutely continuous spectrum for contractive operators
Sergei Treil, Constanze Liaw
We consider contractive operators that are trace class perturbations of a unitary operator . We prove that the dimension functions of the absolutely continuous spectrum of $…
Numerical study of anomalous diffusion of light in semi-crystalline polymer structures
E G Kostadinova, J L Padgett, C D Liaw +2
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability…
Dimension of the exceptional set in the Aronszajn-Donoghue theorem for finite rank perturbations
Constanze Liaw, Sergei Treil, Alexander Volberg
The classical Aronszajn-Donoghue theorem states that for a rank one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the…
Matrix-valued Aleksandrov--Clark measures and Carathéodory angular derivatives
Constanze Liaw, Robert T. W. Martin, Sergei Treil
This paper deals with families of matrix-valued Aleksandrov--Clark measures , corresponding to purely contractive matrix functi…
Anomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method
J. L. Padgett, E. G. Kostadinova, C. D. Liaw +3
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one…
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…
Properties and Decompositions of Domains for Powers of the Jacobi Differential Operator
Dale Frymark, Constanze Liaw
We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, w…
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.…
Spectral approach to transport in the 2D honeycomb lattice with substitutional disorder
E G Kostadinova, C D Liaw, A S Hering +4
The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the quantum percolation problem, characteriz…
Transport properties of disordered 2D complex plasma crystal
E G Kostadinova, A Cameron, F Guyton +4
In this work, we investigate numerically the transport properties of a 2D complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian…
Hyponormal Toeplitz operators with non-harmonic symbol acting on the Bergman space
Matthew Fleeman, Constanze Liaw
The Toeplitz operator acting on the Bergman space , with symbol is given by , where is the projection from onto the Bergm…
Delocalization in infinite disordered 2D lattices of different geometry
E G Kostadinova, K Busse, N Ellis +4
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices…
Boundary Conditions associated with the General Left-Definite Theory for Differential Operators
Matthew Fleeman, Dale Frymark, Constanze Liaw
In the early 2000's, Littlejohn and Wellman developed a general left-definite theory for certain self-adjoint operators by fully determining their domains and spectral properties.…
General Clark model for finite rank perturbations
Constanze Liaw, Sergei Treil
All unitary perturbations of a given unitary operator by finite rank operators with fixed range can be parametrized by unitary matrices ; this generalizes…
Moment Representations of Type I X2 Exceptional Laguerre Polynomials
Constanze Liaw, Jessica Stewart Kelly, John Osborn
The exceptional orthogonal polynomials (XOP) form a complete set of eigenpolynomials to a differential equation. Despite being complete, the XOP set does not contain polynomi…
Moment Representations of Exceptional Orthogonal Polynomials
Constanze Liaw, Jessica Stewart Kelly, John Osborn
We obtain representations of exceptional orthogonal polynomials through determinants of matrices that have certain adjusted moments as entries. We start out directly from the…