Title

Uncertainty principles as embeddings of modulation spaces

Date of Completion

January 2000

Keywords

Mathematics

Degree

Ph.D.

Abstract

It is shown that the theory of modulation spaces Mp,q m can be extended to the case 0 < p, q ≤ ∞ In particular, these spaces admit an atomic decomposition. A class of uncertainty principles is derived in the form of embeddings of modulation spaces. These embeddings provide practical sufficient conditions for a function to belong to a modulation space. Several counterexamples are provided to demonstrate that the conditions on parameters that guarantee the existence of such embeddings are optimal. Complete continuity of a subclass of such embeddings is proved. Also, a class of embeddings of modulation spaces into Lebesgue and Fourier-Lebesgue spaces is derived. ^