30 citations · 91 across the 25 of their papers we have counts for
34 papers
A Bessel Analog of the Riesz Composition Formula
Christoph Fischbacher, Fritz Gesztesy, Roger Nichols
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the latter.
Weak convergence of spectral shift functions revisited
Carson Connard, Benjamin Ingimarson, Roger Nichols +1
We study convergence of the spectral shift function for the finite interval restrictions of a pair of full-line Schrödinger operators to an interval of the form with…
Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm-Liouville operators
Fritz Gesztesy, Roger Nichols
Using the variational characterization of the principal (i.e., smallest) eigenvalue below the essential spectrum of a lower semibounded self-adjoint operator, we prove strict domai…
The Krein-von Neumann Extension of a Regular Even Order Quasi-Differential Operator
Minsung Cho, Seth Hoisington, Roger Nichols +1
We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression o…
Donoghue -functions for singular Sturm--Liouville operators
Fritz Gesztesy, Lance L. Littlejohn, Roger Nichols +2
Let be a densely defined, closed, symmetric operator in the complex, separable Hilbert space with equal deficiency indices and denote by $\mathcal{N}_i = \ke…
On Absence of Threshold Resonances for Schrodinger and Dirac Operators
Fritz Gesztesy, Roger Nichols
Using a unified approach employing a homogeneous Lippmann-Schwinger-type equation satisfied by resonance functions and basic facts on Riesz potentials, we discuss the absence of th…
The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators
Alan Carey, Fritz Gesztesy, Galina Levitina +3
We derive a limiting absorption principle on any compact interval in for the free massless Dirac operator, in $[L^2(\mathbb…
A survey of some norm inequalities
Fritz Gesztesy, Roger Nichols, Jonathan Stanfill
We survey some classical norm inequalities of Hardy, Kallman, Kato, Kolmogorov, Landau, Littlewood, and Rota of the type \[ \|A f\|_{\mathcal{X}}^2 \leq C \|f\|_{\mathcal{X}} \big\…
The Krein-von Neumann extension revisited
Guglielmo Fucci, Fritz Gesztesy, Klaus Kirsten +3
We revisit the Krein-von Neumann extension in the case where the underlying symmetric operator is strictly positive and apply this to derive the explicit form of the Krein-von Neum…
The product formula for regularized Fredholm determinants
Thomas Britz, Alan Carey, Fritz Gesztesy +3
For trace class operators ( a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the famil…
On self-adjoint boundary conditions for singular Sturm-Liouville operators bounded from below
Fritz Gesztesy, Lance L. Littlejohn, Roger Nichols
We extend the classical boundary values \begin{align*} & g(a) = - W(u_{a}(λ_0,.), g)(a) = \lim_{x \downarrow a} \frac{g(x)}{\hat u_{a}(λ_0,x)}, \\ &g^{[1]}(a) = (p g')(a) = W(\hat…
Explicit Krein Resolvent Identities for Singular Sturm-Liouville Operators with Applications to Bessel Operators
S. Blake Allan, Justin Hanbin Kim, Gregory Michajlyszyn +2
We derive explicit Krein resolvent identities for generally singular Sturm-Liouville operators in terms of boundary condition bases and the Lagrange bracket. As an application of t…
On the Global Limiting Absorption Principle for Massless Dirac Operators
Alan Carey, Fritz Gesztesy, Jens Kaad +4
We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators for all space dimensions , $…
Dirichlet-to-Neumann Maps, Abstract Weyl-Titchmarsh -Functions, and a Generalized Index of Unbounded Meromorphic Operator-Valued Functions
Jussi Behrndt, Fritz Gesztesy, Helge Holden +1
We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter dependent Dirichlet-to-N…
On the index of meromorphic operator-valued functions and some applications
Jussi Behrndt, Fritz Gesztesy, Helge Holden +1
We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-value…
Double operator integral methods applied to continuity of spectral shift functions
Alan Carey, Fritz Gesztesy, Galina Levitina +3
We derive two main results: First, assume that , , , are self-adjoint operators in the Hilbert space , and suppose that converges to and $B_…
Some applications of almost analytic extensions to operator bounds in trace ideals
Fritz Gesztesy, Roger Nichols
Using the Davies-Helffer-Sjöstrand functional calculus based on almost analytic extensions, we address the following problem: Given self-adjoint operators , , in $\math…
Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains
Fritz Gesztesy, Steve Hofmann, Roger Nichols
We discuss stability of square root domains for uniformly elliptic partial differential operators in , with mixed boundary conditions on…
On a problem in eigenvalue perturbation theory
Fritz Gesztesy, Sergey N. Naboko, Roger Nichols
We consider additive perturbations of the type , , where and are self-adjoint operators in a separable Hilbert space and is boun…
On Factorizations of Analytic Operator-Valued Functions and Eigenvalue Multiplicity Questions
Fritz Gesztesy, Helge Holden, Roger Nichols
We study several natural multiplicity questions that arise in the context of the Birman-Schwinger principle applied to non-self-adjoint operators. In particular, we re-prove (and e…
A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensions
Fritz Gesztesy, Roger Nichols
We study the analog of semi-separable integral kernels in of the type $$ K(x,x')=\begin{cases} F_1(x)G_1(x'), & a<x'< x< b, \\ F_2(x)G_2(x'), & a<x<x'<b, \end{cases}…
Inverse Spectral Problems for Schrödinger-Type Operators with Distributional Matrix-Valued Potentials
Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols +2
The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schrödinger-type operators on a half-line fro…
Principal Solutions Revisited
Stephen Clark, Fritz Gesztesy, Roger Nichols
The main objective of this paper is to identify principal solutions associated with Sturm-Liouville operators on arbitrary open intervals , as introduce…
Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions II
Fritz Gesztesy, Marius Mitrea, Roger Nichols +1
The principal aim of this short note is to extend a recent result on Gaussian heat kernel bounds for self-adjoint $L^2(\Om; d^n x)$-realizations, , , of divergen…