J. Toth

activity

20002022

most citedL^p norms of eigenfunctions in the completely integrable case

43 citations · 105 across the 18 of their papers we have counts for

collaborators

26 papers

math.AP2022

Lower bounds for eigenfunction restrictions in lacunary regions

Yaiza Canzani, John A. Toth

Let $(M, g)$ be a compact, smooth Riemannian manifold and ${u_{h}}$ be a sequence of $L^{2}$ -normalized Laplace eigenfunctions that has a localized defect measure $μ$ in the sense tha…

math.AP2021

Lower bounds for Steklov eigenfunctions

Jeffrey Galkowski, John A. Toth

Let $(Ω, g)$ be a compact, analytic Riemannian manifold with analytic boundary $\partial Ω = M .$ We give $L^{2}$ -lower bounds for Steklov eigenfunctions and their restrictions to inter…

math.AP2020★ 1 cited

Non-concentration and restriction bounds for Neumann eigenfunctions of piecewise $C^{\infty}$ bounded planar domains

Hans Christianson, John A. Toth

Let $(Ω, g)$ be a piecewise-smooth, bounded convex domain in $R^{2}$ and consider $L^{2}$ -normalized Neumann eigenfunctions $ϕ_{λ}$ with eigenvalue $λ^{2}$ and $u_{λ} := ϕ_{λ} ∣_{\partial Ω}$ t…

math.AP2018

Pointwise bounds for joint eigenfunctions of quantum completely integrable systems

Jeffrey Galkowski, John A. Toth

Let $(M, g)$ be a compact Riemannian manifold and $P_{1} := - h^{2} Δ_{g} + V (x) - E_{1}$ so that $d p_{1} \neq = 0$ on $p_{1} = 0$ . We assume that $P_{1}$ is quantum completely integrable in the sense that th…

math.AP2018★ 1 cited

Reverse Agmon estimates and nodal intersection bounds in forbidden regions

John A. Toth, Xianchao Wu

Let $(M, g)$ be a compact, Riemannian manifold and $V \in C^{\infty} (M; R)$ . Given a regular energy level $E > min V$ , we consider $L^{2}$ -normalized eigenfunctions, $u_{h},$ …

math.AP2017

Nodal intersections and Geometric Control

John A. Toth, Steve Zelditch

This article contains a generalization of the authors' results on numbers of nodal points of eigenfunctions on "good curves" in analytic plane domains (arXiv:0710.0101). The term `…