Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of
functions with applications in time-frequency analysis, the theory of pseudo-differential …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of
functions obtained from one Gaussian by time-and frequency shifts. Each of these is well …

We present a new bound for suprema of a special type of chaos process indexed by a set of
matrices, which is based on a chaining method. As applications we show significantly …

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal
processing and, naturally, mathematics. In a general setting they can be described as frame …

The principle of extension is widespread within mathematics. Starting from simple objects
one constructs more sophisticated ones, with a kind of natural embedding from the set of old …

This paper provides algebraic and analytic, as well as numerical arguments why and how
double preconditioning of the Gabor frame operator yields an efficient method to compute …

Without doubt function spaces play a crucial role in Harmonic Analysis. Moreover many
function spaces arose from questions in Fourier analysis. Here we would like to draw the …

Notion of frames and Bessel sequences for metric spaces have been introduced. This notion
is related with the notion of Lipschitz free Banach spaces.\It is proved that every separable …

The relation between mathematics and music has a long and rich history, in-cluding:
Pythagorean harmonic theory, fundamentals and overtones, frequency and pitch, and …