Henrik Ueberschaer

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20222026

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math.AP2026

Unique continuation at infinity for potentials with arbitrary radial growth

Henrik Ueberschaer

Let $G$ be any given continuous positive function on $R_{+}$ . Let $V$ be radial with $∣ V (x) ∣ \leq G (∣ x ∣)$ . We prove a Landis-type theorem for any real-valued solution of $Δu=…

math.AP2026

On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators

Henrik Ueberschaer, Omer Friedland

Let $Ω \subset R^{d}$ be any open set. We consider solutions of $H ψ_{λ} = λ ψ_{λ}$ , $λ \in C$ , where $H$ is an $m$ th order complex constant-coefficient elliptic partial differ…

math.AP2025

A Liouville-type theorem for Schrödinger equations with nonnegative potential

Henrik Ueberschaer

Let $u$ be a solution of $Δ u = V u$ on $R^{d}$ , where $V$ be continuous, nonnegative and bounded. We prove that the condition $\int_{r_{j} \leq ∣ x ∣ \leq r_{j} + 1} ∣ u (x) ∣^{2} d x \to 0,$ al…

math.AP2024

Local $l^{\infty}$ bounds for eigenfunctions of complex elliptic operators via diophantine problems

Omer Friedland, Henrik Ueberschaer

We prove local bounds on the amplitude of eigen- functions of complex constant-coefficient elliptic operators with a smooth potential on an arbitrary open subset of \R^d by estimat…

Unique continuation at infinity for potentials with arbitrary radial growth

On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators

A Liouville-type theorem for Schrödinger equations with nonnegative potential

Local l∞ bounds for eigenfunctions of complex elliptic operators via diophantine problems

Local $l^{\infty}$ bounds for eigenfunctions of complex elliptic operators via diophantine problems