ARI guest talk by Dimitri Bytchenkoff, Université de Lorraine
31. October 2018:
ARI Seminar Room, Wohllebengasse 12-14, ground floor
The main purpose of this presentation is to introduce a new family of quasi-Banach spaces – which I shall call wave packet smoothness spaces – that includes many of those spaces of functions that can be characterised by sparsity of their cDimitoefficients with respect to various frames. First of all I shall introduce three major building blocks of which the wave packet smoothness spaces are made, namely an almost structured covering of the frequency plane, regular partition of unity subordinate to the covering and a covering-moderate weight. I shall then define what I shall call wave packet systems and discuss the conditions under which they will be both Banach frames and atomic decompositions of the wave packet smoothness spaces. Finally I shall establish the conditions under which one wave packet smoothness space will be embedded in the other or in Besov or Sobolev space.