The road to equal-norm Parseval frames

Journal of Functional Analysis

Volumn 258, Issue 2, 2010, Pages 397-420

  Bodmann, Bernhard G ^a   Casazza, Peter G ^b  

^a University of Houston   (United States)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

Bures distance; Frame energy; Frames; Nearly equal norm; Nearly Parseval; ODE system; Switching equivalence

Indexed keywords

EID: 70350604547     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.08.015     Document Type: Article

References (33)

1. Appleby D.M. SIC-POVMs and the extended Clifford group. J. Math. Phys. 46 (2005) 052107/1-29
2. Balan R. Equivalence relations and distances between Hilbert frames. Proc. Amer. Math. Soc. 127 8 (1999) 2353-2366
3. Benedetto J.J., and Fickus M. Finite normalized tight frames. Adv. Comput. Math. 18 (2003) 357-385
4. Benedetto J.J., Powell A.M., and Yilmaz O. Sigma-Delta quantization and finite frames. IEEE Trans. Inform. Theory 52 (2006) 1990-2005
5. *-encoding. IEEE Trans. Inform. Theory 53 (2007) 4738-4749
6. Bodmann B.G., and Paulsen V.I. Frames, graphs and erasures. Linear Algebra Appl. 404 (2005) 118-146
7. Bodmann B.G., and Paulsen V.I. Frame paths and error bounds for sigma-delta quantization. Appl. Comput. Harmon. Anal. 22 (2007) 176-197
8. Casazza P.G. Modern tools for Weyl-Heisenberg (Gabor) frame theory. Adv. Imaging Electron Phys. 115 (2001) 1-127
9. Casazza P.G. Custom building finite frames. Wavelets, Frames and Operator Theory. College Park, MD, 2003. Contemp. Math. vol. 345 (2004), Amer. Math. Soc., Providence, RI 61-86
10. Casazza P.G., Fickus M., Kovačević J., Leon M., and Tremain J. A physical interpretation of tight frames. In: Heil C. (Ed). Harmonic Analysis and Applications (2006), Birkhäuser, Boston 51-76
11. Casazza P., and Kovačević J. Equal-norm tight frames with erasures. Frames. Adv. Comput. Math. 18 (2003) 387-430
12. Casazza P., and Kutyniok G. A generalization of Gram Schmidt orthogonalization generating all Parseval frames. Adv. Comput. Math. 18 (2007) 65-78
13. Casazza P., and Leonhard N. Classes of finite equal norm Parseval frames. Contemp. Math. 451 (2008) 11-31
14. P.G. Casazza, D. Redmond, J. Tremain, Real equiangular frames, in: Information Sciences and Systems (42nd Annual Conference on), Princeton, NJ, 2008, pp. 715-720
15. Christensen O. An Introduction to Frames and Riesz Bases (2003), Birkhäuser, Boston
16. Duffin R.J., and Schaeffer A.C. A class of nonharmonic Fourier series. Trans. Amer. Math. Soc. 72 (1952) 341-366
17. Flammia S.T. On SIC-POVMs in prime dimensions. J. Phys. A 39 (2006) 13483-13493
18. Goyal V.K., Kovačević J., and Kelner J.A. Quantized frame expansions with erasures. Appl. Comput. Harmon. Anal. 10 (2001) 203-233
19. N: Analysis, synthesis and algorithms. IEEE Trans. Inform. Theory 44 (1998) 16-31
20. Gröchenig K. Foundations of Time-Frequency Analysis. Appl. Numer. Harmon. Anal. (2001), Birkhäuser Boston, Boston, MA
21. Haantjes J. Equilateral point-sets in elliptic two- and three-dimensional spaces. Nieuw Arch. Wiskd. 22 (1948) 355-362
22. Han D., and Larson D. Bases, Frames and Group Representations, vol. 697, Memoirs (2000), Amer. Math. Soc., Providence, RI
23. Holmes R.B., and Paulsen V.I. Optimal frames for erasures. Linear Algebra Appl. 377 (2004) 31-51
24. Janssen A.J.E.M. Zak transforms with few zeroes and the tie. In: Feichtinger H.G., and Strohmer T. (Eds). Advances in Gabor Analysis (2002), Birkhäuser, Boston 31-70
25. Kalra D. Complex equiangular cyclic frames and erasures. Linear Algebra Appl. 419 (2006) 373-399
26. Kovačević J., and Chebira A. An introduction to frames. Foundations and Trends in Signal Processing (2008), NOW publishers
27. Perko L. Differential Equations and Dynamical Systems. second ed. (1996), Springer, New York
28. Renes J.M., Blume-Kohout R., Scott A.J., and Caves C.M. Symmetric informationally complete quantum measurements. J. Math. Phys. 45 (2004) 2171-2180
29. Strohmer Th., and Heath Jr. R.W. Grassmannian frames with applications to coding and communication. Appl. Comput. Harmon. Anal. 14 (2003) 257-275
30. Tropp J.A., Dhillon I.S., Heath Jr. R., and Strohmer T. Structured tight frames via an alternating projection method. IEEE Trans. Inform. Theory 51 (2005) 188-209
31. Welch L. Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory IT-20 (1974) 397-399
32. Xia P., Zhou Sh., and Giannakis G.B. Achieving the Welch bound with difference sets. IEEE Trans. Inform. Theory 51 (2005) 1900-1907
33. G. Zauner, Quantendesigns - Grundzüge einer nichtkommutativen Designtheorie, Doctorial thesis, University of Vienna, 1999