10 papers
Quantitative uniform resolvent estimates
Piero D'Ancona, Jérémy Faupin, David Krejcirik
We derive quantitative uniform resolvent estimates for Schrödinger operators on the half-line with inverse-square potentials, which provide a sharp behaviour in the limit of large…
A reverse Faber--Krahn inequality for the Robin Laplacian with negative boundary parameter: small coupling in all dimensions
Nunzia Gavitone, David Krejcirik, Gloria Paoli
We establish Bareket's conjecture from 1977 for convex domains in all dimensions in the regime of weak boundary coupling. In other words, we consider the Laplace operator, subject…
Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions
Nunzia Gavitone, David Krejcirik, Gloria Paoli
Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain with , we consider the Robin-Laplacian torsional rigidity $Ï_α…
The Laplacian with complex magnetic fields
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is r…
The relativistic rotated harmonic oscillator
A. Balmaseda, D. Krejcirik, J. M. Pérez-Pardo
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real a…
Spectral analysis of Dirac operators for dislocated potentials with a purely imaginary jump
Lyonell Boulton, David Krejcirik, Tho Nguyen Duc
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form where . For …