J. Galkowski

activity

20112026

most citedRestriction Bounds for the Free Resolvent and Resonances in Lossy Scattering

34 citations · 193 across the 55 of their papers we have counts for

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Showing 2020Show all

9 papers · 1 filter

math.SP2020

Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one

Jeffrey Galkowski

In this article we consider asymptotics for the spectral function of Schrödinger operators on the real line. Let $P : L^{2} (R) \to L^{2} (R)$ have the form $$ P:=-\tfrac{…

math.AP2020

Weyl remainders: an application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold $(M, g)$ of dimension $n$ , let…

math.AP2020

Semiclassical resolvent bounds for long range Lipschitz potentials

Jeffrey Galkowski, Jacob Shapiro

We give an elementary proof of weighted resolvent estimates for the semiclassical Schrödinger operator $- h^{2} Δ + V (x) - E$ in dimension $n \neq = 2$ , where $h, E > 0$ . The potentia…

math.AP2020

Outgoing solutions via Gevrey-2 properties

Jeffrey Galkowski, Maciej Zworski

Gajic--Warnick have recently proposed a definition of scattering resonances based on Gevrey-2 regularity at infinity and introduced a new class of potentials for which resonances c…

math.AP2020

Semiclassical resolvent bounds for weakly decaying potentials

Jeffrey Galkowski, Jacob Shapiro

In this note, we prove weighted resolvent estimates for the semiclassical Schrödinger operator $- h^{2} Δ + V (x) : L^{2} (R^{n}) \to L^{2} (R^{n})$ , $n \neq = 2$ . The potential $…

math.AP2020★ 12 cited

Analytic hypoellipticity of Keldysh operators

Jeffrey Galkowski, Maciej Zworski

We consider Keldysh-type operators, $P = x_{1} D_{x_{1}}^{2} + a (x) D_{x_{1}} + Q (x, D_{x^{'}})$ , $x = (x_{1}, x^{'})$ with analytic coefficients, and with $Q (x, D_{x^{'}})$ second order…

math.AP2020★ 8 cited

Growth of high $L^{p}$ norms for eigenfunctions: an application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

This work concerns $L^{p}$ norms of high energy Laplace eigenfunctions, $(- Δ_{g} - λ^{2}) ϕ_{λ} = 0$ , $∥ ϕ_{λ} ∥_{L^{2}} = 1$ . In 1988, Sogge gave optimal estimates on the growth of $∥ ϕ_{λ} ∥_{L^{p}}$ f…

math.AP2020

Lower bounds for Cauchy data on curves in a negatively curved surface

Jeffrey Galkowski, Steve Zelditch

We prove a uniform lower bound on Cauchy data on an arbitrary curve on a negatively curved surface using the Dyatlov-Jin(-Nonnenmacher) observability estimate on the global surface…

math.AP2020★ 2 cited

An introduction to microlocal complex deformations

Jeffrey Galkowski, Maciej Zworski

In this expository article we relate the presentation of weighted estimates in the book of Martinez to the Bergman kernel approach of Sjöstrand. It is meant as an introduction to t…

Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one

Weyl remainders: an application of geodesic beams

Semiclassical resolvent bounds for long range Lipschitz potentials

Outgoing solutions via Gevrey-2 properties

Semiclassical resolvent bounds for weakly decaying potentials

Analytic hypoellipticity of Keldysh operators

Growth of high Lp norms for eigenfunctions: an application of geodesic beams

Lower bounds for Cauchy data on curves in a negatively curved surface

An introduction to microlocal complex deformations

Growth of high $L^{p}$ norms for eigenfunctions: an application of geodesic beams