Uncertainty principles as embeddings of modulation spaces

Authors

Yevgeniy Viktorovich Galperin, University of Connecticut

Date of Completion

January 2000

Keywords

Mathematics

Degree

Ph.D.

Abstract

It is shown that the theory of modulation spaces M^p,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. ^

Recommended Citation

Galperin, Yevgeniy Viktorovich, "Uncertainty principles as embeddings of modulation spaces" (2000). Doctoral Dissertations. AAI9988040.
https://digitalcommons.lib.uconn.edu/dissertations/AAI9988040