Nicolas Frantz

activity

20222026

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4 papers · 1 filter

math-ph2026

The Spectral Shift Function for Non-Self-Adjoint Perturbations

Vincent Bruneau, Nicolas Frantz, François Nicoleau

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by app…

math-ph2025

Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider a non-self adjoint operator of the form $- h^{2} Δ + i (V (x) + α (x) y)$ on the upper half plane $y > 0$ with Dirichlet boundary conditions on ${y = 0}$ with $V \geq 0$ , $V$ …

math-ph2025

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider the non-selfadjoint, semiclassical Schrödinger operator $L (h) := - h^{2} \partial_{x}^{2} + e^{i α} V$ , where $α \in (- π, π)$ and $V : R \to R_{+}$ is even an…

math-ph2023

Scattering theory for some non-self-adjoint operators

Nicolas Frantz

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_{0}$ . We suppose that $H$ is of the form $H = H_{0} + C W C$ where $C$ is a bounded, positive defin…