R. Rahm

activity

20142022

most citedWeighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in

C^{n}

35 citations · 52 across the 13 of their papers we have counts for

collaborators

13 papers

math.SP2022

Sampling The Lowest Eigenfunction to Recover the Potential in a One-Dimensional Schrödinger Equation

Rob Rahm

We consider the BVP $- y " + q y = λ y$ with $y (0) = y (1) = 0$ . The inverse spectral problems asks one to recover $q$ from spectral information. In this paper, we present a very simple met…

math.CA2021

Off-Diagonal Two Weight Bumps for Fractional Sparse Operators

Rob Rahm

In this paper, we continue some recent work on two weight boundedness of sparse operators to the "off-diagonal" setting. We use the new "entropy bumps" introduced in by Treil-Volbe…

math.CA2020

Borderline Weak--Type Estimates for Sparse Bilinear Forms Involving $A_{\infty}$ Maximal Functions

Rob Rahm

For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^{1} (M w)$ into weak-- $L^{1} (w)$ . Our main…

math.CA2018

Weyl Asymptotics for Perturbations of Morse Potential and Connections to the Riemann Zeta Function

Rob Rahm

Let $N (T; V)$ denote the number of eigenvalues of the Schrödinger operator $- y^{''} + V y$ with absolute value less than $T$ . This paper studies the Weyl asymptotics of perturbations of…

hep-ex2018★ 9 cited

Precision measurements of $σ_{B} (e^{+} e^{-} \to K_{S}^{0} K^{\pm} π^{\mp})$ at center-of-mass energies between 3.8 and 4.6 GeV

BESIII Collaboration, M. Ablikim, M. N. Achasov +444

Using data samples collected by the BESIII detector operating at the BEPCII storage ring, we measure the $e^{+} e^{-} \to K_{S}^{0} K^{\pm} π^{\mp}$ Born cross sections at center-of-mass…

math.CA2016

Entropy Bumps and Another Sufficient Condition for the Two--Weight Boundedness of Sparse Operators

Rob Rahm, Scott Spencer

In this short note, we give a very efficient proof of a recent result of Treil-Volberg and Lacey--Spencer giving sufficient conditions for the two-weight boundedness of a sparse op…

math.CA2016★ 1 cited

$A_{p}$ weights and Quantitative Estimates in the Schrödinger Setting

Ji Li, Rob Rahm, Brett D. Wick

Suppose $L = - Δ + V$ is a Schrödinger operator on $R^{n}$ with a potential $V$ belonging to certain reverse Hölder class $R H_{σ}$ with $σ \geq n /2$ . The aim of this paper is to stu…

math.CA2016★ 35 cited

Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in $C^{n}$

Rob Rahm, Edgar Tchoundja, Brett D. Wick

Using modern techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Be…

math.CA2015★ 4 cited

Two-Weight Inequalities for Commutators with Fractional Integral Operators

Irina Holmes, Robert Rahm, Scott Spencer

In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $μ,λ…

math.CA2015★ 2 cited

Some Entropy Bump Conditions for Fractional Maximal and Integral Operators

Robert Rahm, Scott Spencer

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by T…

math.CA2014★ 1 cited

A Reproducing Kernel Thesis for Operators on $ℓ^{2}$ --valued Bergman-type Function Spaces

Robert Rahm

In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on $ℓ^{2}$ --valued Bergman-type spaces. This paper generalizes many well--kno…

math.CA2014

The Essential Norm of Operators on the Bergman Space of Vector--Valued Functions on the Unit Ball

Robert S. Rahm, Brett D. Wick

Let $A_{α}^{p} (B^{n}; C^{d})$ be the weighted Bergman space on the unit ball $B^{n}$ of $C^{n}$ of functions taking values in $C^{d}$ . For $1<p<\inf…

math.CA2014

Compact Operators on Vector-Valued Bergman Space via the Berezin Transform

Robert S. Rahm

In this paper, we characterise compactness of finite sums of finite products of Toeplitz operators acting on the $C^{d}$ -valued weighted Bergman Space, denoted $A_α^{p}(\m…

Sampling The Lowest Eigenfunction to Recover the Potential in a One-Dimensional Schrödinger Equation

Off-Diagonal Two Weight Bumps for Fractional Sparse Operators

Borderline Weak--Type Estimates for Sparse Bilinear Forms Involving A∞​ Maximal Functions

Weyl Asymptotics for Perturbations of Morse Potential and Connections to the Riemann Zeta Function

Precision measurements of σB​(e+e−→KS0​K±π∓) at center-of-mass energies between 3.8 and 4.6 GeV

Entropy Bumps and Another Sufficient Condition for the Two--Weight Boundedness of Sparse Operators

Ap​ weights and Quantitative Estimates in the Schrödinger Setting

Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in Cn

Two-Weight Inequalities for Commutators with Fractional Integral Operators

Some Entropy Bump Conditions for Fractional Maximal and Integral Operators

A Reproducing Kernel Thesis for Operators on ℓ2--valued Bergman-type Function Spaces

The Essential Norm of Operators on the Bergman Space of Vector--Valued Functions on the Unit Ball

Compact Operators on Vector-Valued Bergman Space via the Berezin Transform

Borderline Weak--Type Estimates for Sparse Bilinear Forms Involving $A_{\infty}$ Maximal Functions

Precision measurements of $σ_{B} (e^{+} e^{-} \to K_{S}^{0} K^{\pm} π^{\mp})$ at center-of-mass energies between 3.8 and 4.6 GeV

$A_{p}$ weights and Quantitative Estimates in the Schrödinger Setting

Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in $C^{n}$

A Reproducing Kernel Thesis for Operators on $ℓ^{2}$ --valued Bergman-type Function Spaces