Balian-Low phenomenon for subspace Gabor frames

Journal of Mathematical Physics

Volumn 45, Issue 8, 2004, Pages 3362-3378

  Gabardo, Jean Pierre ^a   Han, Deguang ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544320485     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1768621     Document Type: Article

References (27)

1. Balan, R., Danbechies, I., and Vaisshampayan, V., "The analysis and design of windowed Fourier frame based multiple description encoding schemes," IEEE Trans. Inf. Theory 46, 2491-2536 (2000).
2. Balian, R., "Un principe d'incertitude fort en théorie du signal ou en mécanique quantique," C. R. Acad. Sci. Paris 291, 1357-1362 (1981).
3. Battle, G., "Heisenberg proof of Balian-Low theorem," Lett. Math. Phys. 15, 175-177 (1988).
4. Benedetto, J., Czaja, W., Cadzin'ski, P., and Powell, A., "Balian-Low theorem and regularity of Gabor systems," J. Geom. Anal. 13, 217-232 (2003).
5. 2d," J. Math. Phys. 44, 1735-1750 (2003).
6. Benedetto, J. and Powell, A., "A (p,q) version of Bourgain's theorem," Trans. Am. Math. Soc. (to be published).
7. Casazza, P., "The art of frame theory," Taiwan. J. Math. 4, 129-201 (2000).
8. Casazza, P., "Modern tools for Weyl-Heisenberg frame theory," Adv. Imaging Electron Phys. 115, 1-127 (2001).
9. 2(ℝ)," Proc. Am. Math. Soc. 129, 145-154 (2001).
10. Daubechies, I., "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inf. Theory 36, 961-1005 (1990).
11. Daubechies, I., Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, Philadelphia, PA, 1992).
12. Duffin, R. J. and Schaeffer, A. C., "A class of nonharmonic Fourier series," Trans. Am. Math. Soc. 72, 341-366 (1952).
13. Feichtinger, H. G. and Strohmer, T., eds., "Gabor analysis and algorithms, theory and applications," in Applied and Numerical Harmonic Analysis (Birkhäuser, Boston, 1998).
14. Feichtinger, H. G. and Strohmer, T. eds., "Advances in Gabor analysis," in Applied and Numerical Harmonic Analysis (Birkhäuser, Boston, 2003).
15. Gabardo, J.-P. and Han, D., "Frame representations for group-like unitary operator systems," J. Oper. Theory 49, 223-244 (2003).
16. Gabardo, J. P. and Han, D., "Subspace Weyl-Heisenberg frames," J. Fourier Anal. Appl. 7, 419-433 (2001).
17. Gabardo, J. P. and Han, D. "Aspects of Gabor frames and operator algebras," in Advances in Gabor Analysis, edited by H. G. Feichtinger and T. Strohmer (Birkhäuser, Boston, 2003), pp. 129-152.
18. Gabardo, J. P. and Han, D., "The uniqueness of the dual of Weyl-Heisenberg subspace frames," Appl. Comput. Harmon. Anal. (to be published, 2004).
19. Gabor, D., "Theory of communication," J. Inst. Elec. Eng. (London) 93, 429-457 (1946).
20. Gröchenig, K., Han, D., Heil, C., and Kutynoik, G., "The Balian-Low theorem for symplectic lattices in higher dimensions," Appl. Comput. Harmon. Anal. 13, 169-176 (2002).
21. Janssen, A. J. E. M., "Gabor representation of generalized functions," J. Math. Anal. Appl. 83, 377-394 (1981).
22. Janssen, A. J. E. M., "On generating tight Gabor frames at critical density," J. Fourier Anal. Appl. 9, 175-214 (2003).
23. Low, F. "Complete sets of wave packets," in A Passion for Physics-Essays in Honor of Geoffrey Chew, edited by C. DeTar et al. (World Scientific, Singapore, 1985), pp. 17-22.
24. Rieffel, M. A., "von Neumann algebras associated with pairs of lattices in Lie groups," Math. Ann. 257, 403-418 (1981).
25. d)," Duke Math. J. 89, 237-282 (1997).
26. Takesaki, M., Theory of Operator Algebras I (Springer-Verlag, New York, 1979).
27. Zibulski, M. and Zeevi, Y. Y., "Analysis of multiwindow Gabor-type schemes by frame methods," Appl. Comput. Harmon. Anal. 4, 188-121 (1997).