Explanipedia

Weyl laws for exponentially small singular values of the $\overline{\partial}$ operator Open

Johannes Sjöstrand, Michael Hitrik, Martin Vogel · 2025

We study the number of exponentially small singular values of the semiclassical $\overline{\partial}$ operator on exponentially weighted $L^2$ spaces on the two-dimensional torus. Accurate upper and lower bounds on the number of such singu…

Fractional anisotropic Calderón problem with external data Open

Ali Feizmohammadi, Tuhin Ghosh, Katya Krupchyk, Angkana Rüland, Johannes Sjöstrand , et al. · 2025

In this paper, we solve the fractional anisotropic Calderón problem with external data in the Euclidean space, in dimensions two and higher, for smooth Riemannian metrics that agree with the Euclidean metric outside a compact set. Specific…

Discussing semigroup bounds with resolvent estimates Open

Bernard Helffer, Johannes Sjöstrand, Joe Viola · 2023

The purpose of this paper is to revisit the proof of the Gearhart-Prüss-Huang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the opera…

Tunneling for the $\overline{\partial}$-operator Open

Johannes Sjöstrand, M. Vogel · 2023

We study the small singular values of the $2$-dimensional semiclassical differential operator $P = 2\,\mathrm{e}^{-ϕ/h}\circ hD_{\overline{z}}\circ \mathrm{e}^{ϕ/h}$ on $S^1+iS^1$ and on $S^1+i\mathbb{R}$ where $ϕ$ is given by $\sin y$ and…

Semiclassical Gevrey operators in the complex domain Open

Michael Hitrik, Richard Lascar, Johannes Sjöstrand, Maher Zerzeri · 2022

We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the co…

Large ∣k∣ Behavior of Complex Geometric Optics Solutions to d‐bar Problems Open

Christian Klein, Johannes Sjöstrand, Nikola Stoilov · 2022

Complex geometric optics solutions to a system of d‐bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey‐Stewartson II equations are studied for large values of the spe…

Large $|k|$ behavior for the reflection coefficient for Davey-Stewartson II equations Open

Christian Klein, Johannes Sjöstrand, Nikola Stoilov · 2022

The study of complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey-Stewartson II equations for large values of the sp…

Semiclassical Gevrey operators and magnetic translations Open

Michael Hitrik, Richard Lascar, Johannes Sjöstrand, Maher Zerzeri · 2022

We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas from time frequency analysis, we show that such operators are uniformly bounde…

Improving semi-groups bounds with resolvent estimates Open

Bernard Helffer, Johannes Sjöstrand · 2021

The purpose of this paper is to revisit the proof of the Gearhardt-Prüss-Hwang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on $\Vert S…

Resonances over a potential well in an island Open

Johannes Sjöstrand, Maher Zerzeri · 2021

In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the…

General Toeplitz Matrices Subject to Gaussian Perturbations Open

Johannes Sjöstrand, Martin Vogel · 2020

Large $|k|$ behavior of d-bar problems for domains with a smooth boundary Open

C. Klein, Johannes Sjöstrand, N. Stoilov · 2020

In a previous work on the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with r…

Toeplitz band matrices with small random perturbations Open

Johannes Sjöstrand, Martin Vogel · 2020

The second Weyl coefficient for a first order system Open

Zhirayr Avetisyan, Johannes Sjöstrand, Dmitri Vassiliev · 2020

Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations (Microlocal Analysis and Singular Perturbation Theory) Open

Johannes Sjöstrand, Martin Vogel · 2017

"Microlocal Analysis and Singular Perturbation Theory". October 5～9, 2015. edited by Yoshitsugu Takei, Takashi Aoki, Naofitmi Honda, Kiyoomi Kataoka and Tatsuya Koike. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in f…

Interior Eigenvalue Density of Jordan Matrices with Random Perturbations Open

Johannes Sjöstrand, Martin Vogel · 2017

Large bidiagonal matrices and random perturbations Open

Johannes Sjöstrand, Martin Vogel · 2016

This is a first paper by the authors about the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.

Local analytic regularity in the linearized Calderón problem Open

Johannes Sjöstrand, Günther Uhlmann · 2016

We show that the linearized local Dirichlet-to-Neumann map at a real-analytic potential for measurements made at an analytic open subset of the boundary is injective.

Variational and Perron–Wiener solutions in stratified Lie groups Open

Nawal Mecherout, Naima Boussekkine, Thierry Ramond, Johannes Sjöstrand · 2016

Rational invariant tori and band edge spectra for non-selfadjoint\n operators Open

Michael Hitrik, Johannes Sjöstrand · 2015

We study semiclassical asymptotics for spectra of non-selfadjoint\nperturbations of selfadjoint analytic $h$-pseudodifferential operators in\ndimension 2, assuming that the classical flow of the unperturbed part is\ncompletely integrable. …

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