Chromatic expansions in function spaces

Chromatic Derivatives, Chromatic Expansions and Associated Spaces

This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess th...

Wavelet expansions, function spaces and multifractal analysis

The purpose of this tutorial is to describe the interplay between three subjects: function spaces, wavelet expansions, and multifractal analysis. Some relationships are now classical. Wavelet bases were immediately considered as remarkable by analysts because they are unconditional bases of ‘most’ function spaces. This property is a key feature of the denoising algorithms of Donoho, for instanc...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Greedy expansions in Banach spaces

Expansions of Chromatic Polynomials and Log-concavity

In this paper we present several results and open problems about logconcavity properties of sequences associated with graph colorings. Five polynomials intimately related to the chromatic polynomial of a graph are introduced and their zeros, combinatorial and log-concavity properties are studied. Four of these polynomials have never been considered before in the literature and some yield new ex...