J. Stanfill

activity

20202026

most citedOn domain properties of Bessel-type operators

8 citations · 25 across the 18 of their papers we have counts for

collaborators

21 papers

math-ph2026

The spectral $ζ$ -function of Sturm--Liouville operators with $N$ generalized point potentials

Guglielmo Fucci, Jonathan Stanfill

This work analyzes the spectral zeta function associated with regular and singular Sturm--Liouville operators endowed with $N$ generalized point potentials. The point interactions…

math.SP2026

Complex analytic theory of Sturm-Liouville operators with Schatten $p$ -class resolvents

Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill

We use the theory of entire functions of finite order to prove a universal spectral dependence of the blowup/decay rate of solutions of the Sturm-Liouville eigenvalue equation for…

math.CA2025

An elementary approach to integral inequalities involving higher order derivatives

Bart Rosenzweig, Jonathan Stanfill

Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven…

math.SP2025

Maximally dissipative and self-adjoint extensions of $K$ -invariant operators

Christoph Fischbacher, Bart Rosenzweig, Jonathan Stanfill

We introduce the notion of $K$ -invariant operators, $S$ , (in a Hilbert space) with respect to a bounded and boundedly invertible operator $K$ defined via $K^{*} S K = S$ . Conditions such…

math.CA2025

$ζ$ -functions via contour integrals and universal sum rules

Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill

This work develops an analytic framework for the study of the $ζ$ -function associated with general sequences of complex numbers. We show that a contour integral representation, com…

math-ph2024

The exotic structure of the spectral $ζ$ -function for the Schrödinger operator with Pöschl--Teller potential

Guglielmo Fucci, Jonathan Stanfill

This work focuses on the analysis of the spectral $ζ$ -function associated with a Schrödinger operator endowed with a Pöschl--Teller potential. We construct the spectral $ζ$ -functio…

math.SP2024

Nonnegative extensions of Sturm-Liouville operators with an application to problems with symmetric coefficient functions

Christoph Fischbacher, Jonathan Stanfill

The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide…

math.AP2024

Factorizations and Power Weighted Rellich and Hardy--Rellich-Type Inequalities

Fritz Gesztesy, Michael M. H. Pang, Jake Parmentier +1

We revisit and extend a variety of inequalities related to power weighted Rellich and Hardy--Rellich inequalities, including an inequality due to Schmincke.

math-ph2024★ 2 cited

The spectral $ζ$ -function for quasi-regular Sturm--Liouville operators

Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill

In this work we analyze the spectral $ζ$ -function associated with the self-adjoint extensions, $T_{A, B}$ , of quasi-regular Sturm--Liouville operators that are bounded from below. B…

math.AP2024★ 1 cited

Logarithmic Refinements of a Power Weighted Hardy--Rellich-Type Inequality

Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill

The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on $n$ -dimensional balls, valid for the largest variety of u…

math.SP2024

Finer limit circle/limit point classification for Sturm-Liouville operators

Mateusz Piorkowski, Jonathan Stanfill

In this paper we introduce an index $ℓ_{c} \in N_{0} \cup {\infty}$ which we call the `regularization index' associated to the endpoints, $c \in {a, b}$ , of no…

math.CA2023

The Jacobi operator on $(- 1, 1)$ and its various $m$ -functions

Fritz Gesztesy, Lance L. Littlejohn, Mateusz Piorkowski +1

We offer a detailed treatment of spectral and Weyl-Titchmarsh-Kodaira theory for all self-adjoint Jacobi operator realizations of the differential expression \begin{align*} τ_{α,β}…

math.CA2021★ 1 cited

The Jacobi operator and its Donoghue $m$ -functions

Fritz Gesztesy, Mateusz Piorkowski, Jonathan Stanfill

In this paper we construct Donoghue $m$ -functions for the Jacobi differential operator in $L^{2} ((- 1, 1); (1 - x)^{α} (1 + x)^{β} d x)$ , associated to the differential expression \begi…

math.SP2021

Donoghue $m$ -functions for singular Sturm--Liouville operators

Fritz Gesztesy, Lance L. Littlejohn, Roger Nichols +2

Let $A ˙$ be a densely defined, closed, symmetric operator in the complex, separable Hilbert space $H$ with equal deficiency indices and denote by $\mathcal{N}_i = \ke…

math.CA2021★ 8 cited

On domain properties of Bessel-type operators

Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill

Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $1/ sin^{2} (x)$ on the finite interval $(0, π)$ , we now take a closer l…

math.FA2021★ 5 cited

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\…

math.FA2021

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…

math.SP2021★ 7 cited

Bessel-Type Operators and a refinement of Hardy's inequality

Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill

The principal aim of this paper is to employ Bessel-type operators in proving the inequality \begin{align*} \int_0^πdx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^πdx \, \dfrac{|f(x)|^2}{…

math.CO2021

Partitions With Designated Summands Not Divisible by $2^{l}$ , $2$ , and $3^{l}$ Modulo $2$ , $4$ , and $3$

Daniel Herden, Mark R. Sepanski, Jonathan Stanfill +4

Numerous congruences for partitions with designated summands have been proven since first being introduced and studied by Andrews, Lewis, and Lovejoy. This paper explicitly charact…

math.SP2021

Spectral zeta-Functions and zeta-Regularized Functional Determinants for Regular Sturm-Liouville Operators

Guglielmo Fucci, Fritz Gesztesy, Klaus Kirsten +1

The principal aim in this paper is to employ a recently developed unified approach to the computation of traces of resolvents and $ζ$ -functions to efficiently compute values of spe…

math.CO2020★ 1 cited

Counting the parts divisible by k in all the partitions of n whose parts have multiplicity less than k

Daniel Herden, Mark R. Sepanski, Jonathan Stanfill +7

Recent results by Andrews and Merca on the number of even parts in all partitions of n into distinct parts, a(n), were derived via generating functions. This paper extends these re…

The spectral ζ-function of Sturm--Liouville operators with N generalized point potentials

Complex analytic theory of Sturm-Liouville operators with Schatten p-class resolvents

An elementary approach to integral inequalities involving higher order derivatives

Maximally dissipative and self-adjoint extensions of K-invariant operators

ζ-functions via contour integrals and universal sum rules

The exotic structure of the spectral ζ-function for the Schrödinger operator with Pöschl--Teller potential

Nonnegative extensions of Sturm-Liouville operators with an application to problems with symmetric coefficient functions

Factorizations and Power Weighted Rellich and Hardy--Rellich-Type Inequalities

The spectral ζ-function for quasi-regular Sturm--Liouville operators

Logarithmic Refinements of a Power Weighted Hardy--Rellich-Type Inequality

Finer limit circle/limit point classification for Sturm-Liouville operators

The Jacobi operator on (−1,1) and its various m-functions

The Jacobi operator and its Donoghue m-functions

Donoghue m-functions for singular Sturm--Liouville operators

On domain properties of Bessel-type operators

A survey of some norm inequalities

The Krein-von Neumann extension revisited

Bessel-Type Operators and a refinement of Hardy's inequality

Partitions With Designated Summands Not Divisible by 2l, 2, and 3l Modulo 2, 4, and 3

Spectral zeta-Functions and zeta-Regularized Functional Determinants for Regular Sturm-Liouville Operators

Counting the parts divisible by k in all the partitions of n whose parts have multiplicity less than k

The spectral $ζ$ -function of Sturm--Liouville operators with $N$ generalized point potentials

Complex analytic theory of Sturm-Liouville operators with Schatten $p$ -class resolvents

Maximally dissipative and self-adjoint extensions of $K$ -invariant operators

$ζ$ -functions via contour integrals and universal sum rules

The exotic structure of the spectral $ζ$ -function for the Schrödinger operator with Pöschl--Teller potential

The spectral $ζ$ -function for quasi-regular Sturm--Liouville operators

The Jacobi operator on $(- 1, 1)$ and its various $m$ -functions

The Jacobi operator and its Donoghue $m$ -functions

Donoghue $m$ -functions for singular Sturm--Liouville operators

Partitions With Designated Summands Not Divisible by $2^{l}$ , $2$ , and $3^{l}$ Modulo $2$ , $4$ , and $3$