Classification of Finite Group-Frames and Super-Frames

Abstract Given a finite group $G$ , we examine the classification of all frame representations of $G$ and the classification of all $G$ -frames, i.e., frames induced by group representations of $G$ . We show that the exact number of equivalence classes of $G$ -frames and the exact number of frame representations can be explicitly calculated. We also discuss how to calculate the largest number $L$ such that there exists an $L$ -tuple of strongly disjoint $G$ -frames.

[1]  Akram Aldroubi,et al.  Geometric aspects of frame representations of abelian groups , 2003, math/0308250.

[2]  Deguang Han,et al.  FRAME REPRESENTATIONS FOR GROUP-LIKE UNITARY OPERATOR SYSTEMS , 2003 .

[3]  Yonina C. Eldar,et al.  Geometrically uniform frames , 2001, IEEE Trans. Inf. Theory.

[4]  Deguang Han,et al.  The uniqueness of the dual of Weyl-Heisenberg subspace frames , 2004 .

[5]  T. Strohmer.  Approximation of Dual Gabor Frames, Window Decay, and Wireless Communications , 2000, math/0010244.

[6]  Ingrid Daubechies,et al.  A study of weyl-heisenberg and wavelet frames , 1998 .

[7]  F. G. W. BROWN,et al.  The Theory of Group Representations , 1940, Nature.

[8]  Deguang Han,et al.  Approximations for Gabor and wavelet frames , 2003 .

[9]  Babak Hassibi,et al.  Representation theory for high-rate multiple-antenna code design , 2001, IEEE Trans. Inf. Theory.

[10]  P. Casazza,et al.  The Kadison–Singer Problem in mathematics and engineering , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Jean-Pierre Gabardo,et al.  Subspace Weyl-Heisenberg frames , 2001 .

[12]  Jean-Pierre Gabardo,et al.  Gabor frames and operator algebras , 2000, SPIE Optics + Photonics.

[13]  P. Casazza,et al.  Uniform Tight Frames with Erasures , 2004 .

[14]  Vivek K Goyal,et al.  Quantized Frame Expansions with Erasures , 2001 .

[15]  Jelena Kovacevic,et al.  Uniform tight frames for signal processing and communication , 2001, SPIE Optics + Photonics.