arXiv subjects

Evanthia Carypis

Publications and source records attributed to Evanthia Carypis.

3 recordsLinked to original sources

arXiv2018

Cohen class of time-frequency representations and operators: boundedness and uncertainty principles

This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered. For these operators, which include all usual quantizations, we prove a boundedness result in the $L^p$ functional setting and a form of uncertainty principle analogous to that for localization operators.

math.FA↗

arXiv2016

Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians

We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand--Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand--Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.

math.AP↗

arXiv2015

Two Aspects of the Donoho-Stark Uncertainty Principle

We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical Donoho-Stark estimate in two different aspects: a better general lower bound and a lower bound in dependence on the signal itself.

math.FA↗