8 citations · 25 across the 12 of their papers we have counts for
12 papers
Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities
Jussi Behrndt, Dale Frymark, Markus Holzmann +1
For a family of self-adjoint Dirac operators subject to generalized MIT bag boundary conditions on domains in it is shown that…
Spectral analysis of the Dirac operator with a singular interaction on a broken line
Dale Frymark, Markus Holzmann, Vladimir Lotoreichik
We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar -shell interaction of strength $τ\in\mathb…
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…
The Spectrum of Self-Adjoint Extensions associated with Exceptional Laguerre Differential Expressions
Dale Frymark, Jessica Stewart Kelly
Exceptional Laguerre-type differential expressions make up an infinite class of Schrödinger operators having rational potentials and one limit-circle endpoint. In this manuscript,…
Self-adjointness of the 2D Dirac operator with singular interactions supported on star-graphs
Dale Frymark, Vladimir Lotoreichik
We consider the two-dimensional Dirac operator with Lorentz-scalar -shell interactions on each edge of a star-graph. An orthogonal decomposition is performed which shows such an…
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…
Boundary Triples and Weyl -functions for Powers of the Jacobi Differential Operator
Dale Frymark
The abstract theory of boundary triples is applied to the classical Jacobi differential operator and its powers in order to obtain the Weyl -function for several self-adjoint ex…
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…
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.…