# Partial Differential Equations, Spectral Theory, and Mathematical Physics

The Ari Laptev Anniversary Volume

## Editors

### Pavel Exner

Czech Technical University, Prague and Czech Academy of Sciences, Řež, Czech Republic### Rupert L. Frank

California Institute of Technology, Pasadena, USA and Ludwig-Maximilians-Universität München, Germany### Fritz Gesztesy

Baylor University, Waco, USA### Helge Holden

Norwegian University of Science and Technology, Trondheim, Norway### Timo Weidl

Universität Stuttgart, Germany

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This volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory.

In brief, the topics covered include Friedrichs, Hardy, and Lieb–Thirring inequalities, eigenvalue bounds and asymptotics, Feshbach–Schur maps and perturbation theory, scattering theory and orthogonal polynomials, stability of matter, electron density estimates, Bose–Einstein condensation, Wehrl-type entropy inequalities, Bogoliubov theory, wave packet evolution, heat kernel estimates, homogenization, d-bar problems, Brezis–Nirenberg problems, the nonlinear Schrödinger equation in magnetic fields, classical discriminants, and the two-dimensional Euler–Bardina equations. In addition, Ari’s multifaceted service to the mathematical community is also touched upon.

Altogether the volume presents a collection of research articles which will be of interest to any active scientist working in one of the above mentioned fields.