Classifying Tight Weyl-Heisenberg Frames
Peter G. Casazza, Ole Christensen
Abstract
A Weyl-Heisenberg frame for L2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).
Create a lesson
Related papers
Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in c0 and 1
Parveen Kumar, Ankit Kumar
Bourgain-Rosenthal-Schechtman spaces in rearrangement-invariant and Hardy spaces
Konstantinos Konstantos, Pavlos Motakis, Thomas Speckhofer
The tensor product of the Fremlin tensor product of Banach lattice algebras
Jamel Jaber, Marwa Troudi
Gaussian inequalities with different covariance matrices - the Heterovariant Gaussian Brunn-Minkowski inequality
Emanuel Milman, Shohei Nakamura, Hiroshi Tsuji
Quasinormal and hyponormal operators in the β(H)-class
Ramesh Golla, Hiroyuki Osaka, Shanola S. Sequeira
A Vector-Valued Extension of a Theorem of Marciszewski
Leandro Candido