Uncertainty Principle for Rational Functions in Hardy Spaces

Dan Xiong; Li Chai; Jingxin Zhang

ICASSP 2018accepted0 citations

Uncertainty Principle for Rational Functions in Hardy Spaces

Abstract

Uncertainty principles in finite dimensional vector space have been studied extensively, however they cannot be applied to sparse representation of rational functions. This paper considers the sparse representation for a rational function under a pair of orthonormal rational function bases. We prove the uncertainty principle concerning pairs of compressible representation of rational functions in the infinite dimensional function space. The uniqueness of compressible representation using such pairs is provided as a direct consequence of uncertainty principle.

BibTeX

@inproceedings{icassp2018_uncertaintyprinc,
  title = {Uncertainty Principle for Rational Functions in Hardy Spaces},
  author = {Dan Xiong and Li Chai and Jingxin Zhang},
  booktitle = {ICASSP 2018},
  year = {2018}
}