Some unexpected behaviors of operators with small time-frequency dispersion

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Toeplitz operators with matrix-valued symbols and some (unexpected) applications

We discuss the eigenvalue distribution in the Weyl sense of general matrix-sequences associated to a symbol. As a specific case we consider Toeplitz sequences generated by matrix-valued (non Hermitian) bounded functions. We show that the canonical distribution can be proved under mild assumptions on the spectral range of the given symbol. Finally some applications are introduced and discussed.

Time - Frequency Analysis of Localization Operators

Time Frequency Localization of Trigonometric Hermite Operators

In this paper, localization properties of trigonometric polynomial Hermite operators are discussed. In particular, time frequency uncertainty and operator norms are compared for the diierent types of fundamental interpolants which serve as scaling functions for a trigono-metric multiresolution analysis. x1. Introduction Recently, several diierent approaches to periodic multiresolution analyses ...

Frequency dispersion of small-amplitude capillary waves in viscous fluids.

This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of capillary waves in the underdamped regime is proposed, including predictions for the wave nu...