We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2
sense, solutions of the free stationary and dynamical Schroedinger equations. In this note …

In this paper, we present some novel and intriguing findings on the geometric structures of
Laplacian eigenfunctions and their deep relationship to the quantitative behaviours of the …

Much recent interest has focused on" open" dynamical systems, in which a classical map or
flow is considered only until the trajectory reaches a" hole", at which the dynamics is no …

We investigate the stability properties of strongly continuous semigroups generated by
operators of the form A− BB∗, where A is the generator of a contraction semigroup and B is …

We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational
polygon. The modulus squared of the eigenfunctions defines a sequence of probability …

We prove Strichartz estimates with a loss of derivatives for the Schrödinger equation on
polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions …

We give a complete characterization of the relationship between the shape of a Euclidean
polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tables …

This work is concerned with operators of the type AD Qc acting in domains 0. 0; H/Â Rd RC:
The diffusion coefficient Qc> 0 depends on one coordinate y 2. 0; H/and is bounded but may …

We characterize quantum limits and semi-classical measures corresponding to sequences
of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary …