A (p, q) version of bourgain's theorem

Transactions of the American Mathematical Society

Volumn 358, Issue 6, 2006, Pages 2489-2505

  Benedetto, John J ^a   Powell, Alexander M ^b  

^a Bldg 142   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Fourier analysis; Gabor analysis; The uncertainty principle

Indexed keywords

EID: 33744742871     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03737-2     Document Type: Article

References (25)

1. [Bal] R. Balian, Un precipe d'incertitude fort en théorie du signal ou en méchanique quantique, C.R. Acad. Sci. Paris, 292 (20): 1357-1362, 1981. MR0644367 (83a:94009)
2. [B1] J. J. Benedetto, Frame decompositions, sampling, and uncertainty principle inequalities, in Wavelets: Mathematics and Applications, Stud. Adv. Math., CRC, Boca Raton, FL, 1994. MR1247519 (941:94005)
3. 2d, J. Math. Phys., 44 (4): 1735-1750, 2003. MR1963822 (2004a:42041)
4. [BCGP] J. J. Benedetto, W. Czaja, P. Gadziński, A. M. Powell, The Balian-Low theorem and regularity of Gabor systems, J. Geom. Anal. 13 (2): 217-232, 2003. MR1967026 (2004b:42071)
5. 2 and related spaces, in Wavelets: Mathematics and Applications, Stud. Adv. Math., CRC, Boca Raton, FL, 1994. MR1247515 (941:42040)
6. [Bou] J. Bourgain, A remark on the uncertainty principle for Hilbertian basis, J. Funct. Anal., 79 (1): 136-143, 1988. MR0950087 (89f:81025)
7. [C] O. Christensen, Frames, Riesz bases, and discrete Gabor/wavelet expansions, Bull. Amer. Math. Soc. (N.S.), 38 (3): 273-291, 2001. MR1824891 (2002c:42040)
8. [CP] M. G. Cowling and J. F. Price, Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality, SIAM J. Math. Anal., 15 (1): 151-165, 1984. MR0728691 (86g:42002a)
9. [DJ] I. Daubechies and A. J. E. M. Janssen, Two theorems on lattice expansions, IEEE Trans. Inform. Theory, 39 (1): 3-6, 1993. MR1211486 (94f:94001)
10. [F] G. B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1989. MR0983366 (92k:22017)
11. [FG1] H. Feichtinger and K. Gröchenig, Gabor frames and time-frequency analysis of distributions, J. Func. Anal., 146: 464-495, 1997. MR1452000 (98k:42041)
12. [FG2] H. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions. I., J. Func. Anal., 86: 307-340, 1989. MR1021139 (91g:43011)
13. [FS] G. B. Folland and A. Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl., 3 (3): 207-238, 1997. MR1448337 (98f:42006)
14. [GH] J.-P. Gabardo and D. Han, Balian-Low phenomenon for subspace Gabor frames, Preprint, 2004.
15. [G1] K. Gröchenig, An uncertainty principle related to the Poisson summation formula, Studia Math., 121 (1): 87-104, 1996. MR1414896 (98a:42007)
16. [G2] K. Gröchenig, Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkäuser, Boston, MA, 2001. MR1843717 (2002h:42001)
17. [GHHK] K. Gröchenig, D. Han, C. Heil and G. Kutyniok, The Balian-Low theorem for symplectic lattices in higher dimensions, Appl. Comput. Harmon. Anal., 13 (2): 169-176, 2002. MR1942751 (20031:42041)
18. [HJ] V. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 28, Springer Verlag, Berlin, 1994. MR1303780 (96c:42001)
19. [HRT] G. Heil, J. Ramanathan and R. Topiwala, Linear independence of time-frequency translates, Proc. Amer. Math. Soc., 124 (9): 2787-2795, 1996. MR1327018 (96k:42039)
20. [J] S. Jaffard, Propriétés des matrices "bien localisées" près de leur diagonale et quelques applications, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (5):461-476, 1990. MR1138533 (93h:47035)
21. [LM] P. G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana, 2 (1-2):1-18, 1986. MR0864650
22. [Lo] F. Low, Complete sets of wave packets. In C. De Tar, editor, A Passion for Physics -Essays in Honor of Geoffrey Chew, pages 17-22. World Scientific, Singapore, 1985.
23. n, CBMS Regional Conference Series in Mathematics, 63. Published for the Conference Board of the Mathematical Sciences, Washington, DC, by the American Mathematical Society, Providence, RI, 1986. MR0840468 (87f:32013)
24. [S] T. Strohmer, Four short stories about Toeplitz matrix calculations, Linear Algebra Appl., 343/344: 321-344, 2002. MR1878948 (2002k:47060)
25. [Y] R. M. Young, An Introduction to Nonharmonic Fourier Series, revised first edition, Academic Press, San Diego, CA, 2001. MR1836633 (2002b:42001)