297 research outputs found
Landau's necessary density conditions for LCA groups
H. Landau's necessary density conditions for sampling and interpolation may
be viewed as a general principle resting on a basic fact of Fourier analysis:
The complex exponentials ( in ) constitute an
orthogonal basis for . The present paper extends Landau's
conditions to the setting of locally compact abelian (LCA) groups, relying in
an analogous way on the basics of Fourier analysis. The technicalities--in
either case of an operator theoretic nature--are however quite different. We
will base our proofs on the comparison principle of J. Ramanathan and T.
Steger
Frame Constants of Gabor Frames near the Critical Density
We consider Gabor frames generated by a Gaussian function and describe the
behavior of the frame constants as the density of the lattice approaches the
critical value
On the Usefulness of Modulation Spaces in Deformation Quantization
We discuss the relevance to deformation quantization of Feichtinger's
modulation spaces, especially of the weighted Sjoestrand classes. These
function spaces are good classes of symbols of pseudo-differential operators
(observables). They have a widespread use in time-frequency analysis and
related topics, but are not very well-known in physics. It turns out that they
are particularly well adapted to the study of the Moyal star-product and of the
star-exponential.Comment: Submitte
Linear perturbations of the Wigner transform and the Weyl quantization
We study a class of quadratic time-frequency representations that, roughly
speaking, are obtained by linear perturbations of the Wigner transform. They
satisfy Moyal's formula by default and share many other properties with the
Wigner transform, but in general they do not belong to Cohen's class. We
provide a characterization of the intersection of the two classes. To any such
time-frequency representation, we associate a pseudodifferential calculus. We
investigate the related quantization procedure, study the properties of the
pseudodifferential operators, and compare the formalism with that of the Weyl
calculus.Comment: 38 pages. Contributed chapter for volume on the occasion of Luigi
Rodino's 70th birthda
Abstract composition laws and their modulation spaces
On classes of functions defined on R^2n we introduce abstract composition
laws modelled after the pseudodifferential product of symbols. We attach to
these composition laws modulation mappings and spaces with useful algebraic and
topological properties.Comment: 19 page
Conormal distributions in the Shubin calculus of pseudodifferential operators
We characterize the Schwartz kernels of pseudodifferential operators of
Shubin type by means of an FBI transform. Based on this we introduce as a
generalization a new class of tempered distributions called Shubin conormal
distributions. We study their transformation behavior, normal forms and
microlocal properties.Comment: 23 page
- …