We study the eigenvalues and eigenfunctions of the time-frequency localization operator $
H_\Omega $ on a domain $\Omega $ of the time-frequency plane. The eigenfunctions are …

One method by which the time–frequency content of a signal can be measured is by the
Gabor (or windowed Fourier) transform. It is defined as the Fourier transform of the product …

We investigate an inverse problem in time-frequency localization: the approximation of the
symbol of a time-frequency localization operator from partial spectral information by the …

Prolate spheroidal wave functions are an orthogonal family of bandlimited functions on R
that have the highest concentration within a specific time interval. They are also identified as …

We consider the localization of eigenfunctions for the operator L=− div A grad+ V on a
Lipschitz domain Ω and, more generally, on manifolds with and without boundary. In earlier …

Time-variant filters based on Calderón and Gabor reproducing formulas are important tools
in time-frequency analysis. The paper studies the behavior of the eigenvalues of these …

The Laplacian∆(∂ 2∂ x2+∂ 2∂ y2 in the plane) is one of the most basic operators in all of
mathematical analysis. It can be used to construct the important spacetime equations of …

A classical result of time–frequency analysis, obtained by Daubechies in 1988, states that
the eigenfunctions of a time–frequency localization operator with circular localization …

The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution
of eigenvalues, is one of the central problems in the spectral theory of partial differential …

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