Schrödinger Operators, Spectral Analysis and Number Theory

This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential.

S. Albeverio and R. Weder, Introduction to the scientific contributions in the book.- S. Albeverio and I. Karabash, Asymptotics of random resonances generated by a point process of delta-interactions.- M. S. Ashbaugh, F. Gesztesy, L. Hermi, K. Kirsten, L. Littlejohn and H. Tossounian, Green's function and Euler's formula for ¿(2n).- P. Bérard and B. Helffer, On Courant's nodal domain property for linear combinations of eigenfunctions.- Part II: A. Boutet de Monvel and L. Zielinski, Asymptotic behavior of large eigenvalues of the two-photon Rabi model.- J.-Michel Combes and P. Hislop, Some remarks on spectral averaging and the local density of states for random Schrödinger operators on L²(Rd).- R. Froese and I. Herbst, Resonances in the one dimensional Stark effect in the limit of small field.- P. Kurasov and J. Muller, On the spectral gap for networks of beams.- K. Nicholas Leibovic, Some notes in the context of binocular space perception.- T. Paul, Symbolic calculus for singular curve operators.- Y. N. Petridis and M. S. Risager, Higher order deformations of hyperbolic spectra.- S. K. Sekatskii, On the generalized Li's criterion equivalent to the Riemann hypothesis and its first applications.- M. Spreafico and A. Zaccagnini, Regularizing infinite products by the asymptotics of finite products.- R. Weder, Trace maps under weak regularity assumptions.