M. Goldberg

activity

20032023

most citedSchrödinger dispersive estimates for a scaling-critical class of potentials

52 citations · 427 across the 30 of their papers we have counts for

collaborators

32 papers

math.AP2023

Spectral multipliers III: Endpoint bounds, intertwining operators, and twisted Hardy spaces

Marius Beceanu, Michael Goldberg

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $R^{3}$ to the case of perturbed Hamiltonians of the form $H = - Δ + V$ , where $V$ …

math.AP2023★ 2 cited

Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials

M. Burak Erdogan, Michael Goldberg, William R. Green

We prove a family of dispersive estimates for the higher order Schrödinger equation $i u_{t} = (- Δ)^{m} u + V u$ for $m \in N$ with $m > 1$ and $2 m < n < 4 m$ . Here $V$ is a real-valued pote…

math.AP2023

Spectral Multipliers II: Elliptic and Parabolic Operators and Bochner-Riesz Means

Marius Beceanu, Michael Goldberg

We establish estimates for the Poisson kernel, the heat kernel, and Bochner--Riesz means defined in terms of $H = - Δ + V$ , where $V$ is a possibly large rough real-valued scalar potent…

math.AP2022

Spectral multipliers and wave propagation for Hamiltonians with a scalar potential

Marius Beceanu, Michael Goldberg

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $R^{3}$ to the case of perturbed Hamiltonians of the form $- Δ + V$ , where $V$ i…

math.AP2022★ 11 cited

Counterexamples to $L^{p}$ boundedness of wave operators for classical and higher order Schrödinger operators

M. Burak Erdogan, Michael Goldberg, William R. Green

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 4 m - 1$ , $m \in N$ . We show that for any $\frac{2n}{…

math.AP2020★ 15 cited

On the $L^{p}$ boundedness of the Wave Operators for fourth order Schrödinger operators

Michael Goldberg, William R. Green

We consider the fourth order Schrödinger operator $H = Δ^{2} + V (x)$ in three dimensions with real-valued potential $V$ . Let $H_{0} = Δ^{2}$ , if $V$ decays sufficiently and there are no eigenv…

Spectral multipliers III: Endpoint bounds, intertwining operators, and twisted Hardy spaces

Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials

Spectral Multipliers II: Elliptic and Parabolic Operators and Bochner-Riesz Means

Spectral multipliers and wave propagation for Hamiltonians with a scalar potential

Counterexamples to Lp boundedness of wave operators for classical and higher order Schrödinger operators

On the Lp boundedness of the Wave Operators for fourth order Schrödinger operators

Counterexamples to $L^{p}$ boundedness of wave operators for classical and higher order Schrödinger operators

On the $L^{p}$ boundedness of the Wave Operators for fourth order Schrödinger operators