Frames for decomposition spaces generated by a single function (Q486333)

This paper studies the link between discrete sparse representations and smoothness, within the framework of \textit{decomposition smoothness spaces}. Earlier work by the author has given rise to tight frames for smoothness spaces of both Besov and Triebel-Lizorkin type in terms of an infinite sequence \({\mu_k}\) of functions. However, such frames have the disadvantage of being hard to implement as compared to wavelets or Gabor systems that are generated by a small number of functions. In the present work, the author presents a construction of frames for decomposition spaces generated by a \textit{single} function. Moreover, it is also shown that this single generator can be chosen to have compact support.