The structure of shift-modulation invariant spaces: The rational case

Journal of Functional Analysis

Volumn 244, Issue 1, 2007, Pages 172-219

  Bownik, Marcin ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

Dimension function; Dual frame; Frame sequence; Gabor subspace; Range function; Range operator; Riesz sequence; Shift modulation invariant space; Weyl Heisenberg subspace

Indexed keywords

EID: 33846561230     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.11.003     Document Type: Article

References (31)

1. d). J. Funct. Anal. 119 (1994) 37-78
2. n). J. Funct. Anal. 177 (2000) 282-309
3. Bownik M., and Rzeszotnik Z. The spectral function of shift-invariant spaces. Michigan Math. J. 51 (2003) 387-414
4. 2 (R). Proc. Amer. Math. Soc. 129 (2001) 145-154
5. Casazza P., Christensen O., and Janssen A.J.E.M. Weyl-Heisenberg frames, translation invariant systems and the Walnut representation. J. Funct. Anal. 180 (2001) 85-147
6. Christensen O. An Introduction to Frames and Riesz Bases (2003), Birkhäuser Boston, Boston, MA
7. Christensen O., and Eldar Y. Oblique dual frames and shift-invariant spaces. Appl. Comput. Harmon. Anal. 17 (2004) 48-68
8. Christensen O., and Eldar Y. Generalized shift-invariant systems and frames for subspaces. J. Fourier Anal. Appl. 11 (2005) 299-313
9. Daubechies I. Ten Lectures on Wavelets (1992), SIAM, Philadelphia, PA
10. In: Feichtinger H., and Strohmer T. (Eds). Gabor Analysis and Algorithms. Theory and Applications (1998), Birkhäuser Boston, Boston, MA
11. In: Feichtinger H., and Strohmer T. (Eds). Advances in Gabor Analysis (2003), Birkhäuser Boston, Boston, MA
12. Gabardo J.-P., and Han D. Subspace Weyl-Heisenberg frames. J. Fourier Anal. Appl. 7 (2001) 419-433
13. Gabardo J.-P., and Han D. Aspects of Gabor analysis and operator algebras. Advances in Gabor Analysis. Appl. Numer. Harmon. Anal. (2003), Birkhäuser Boston, Boston, MA 129-152
14. Gabardo J.-P., and Han D. Balian-Low phenomenon for subspace Gabor frames. J. Math. Phys. 45 (2004) 3362-3378
15. Gabor D. Theory of communications. J. Inst. Electr. Eng. (London) 93 (1946) 429-457
16. Gröchenig K. Foundations of Time-Frequency Analysis (2001), Birkhäuser, Basel
17. Han D., and Larson D. Frames, bases and group representations. Mem. Amer. Math. Soc. 147 697 (2000)
18. Han D., and Wang Y. Lattice tiling and the Weyl-Heisenberg frames. Geom. Funct. Anal. 11 (2001) 742-758
19. Heil C. Linear independence of finite Gabor systems. In: Heil C. (Ed). Harmonic Analysis and Applications (2006), Birkhäuser Boston, Boston, MA 171-206
20. Helson H. Lectures on Invariant Subspaces (1964), Academic Press, New York/London
21. Janssen A.J.E.M. Duality and biorthogonality for Weyl-Heisenberg frames. J. Fourier Anal. Appl. 1 (1995) 403-436
22. Janssen A.J.E.M. On rationally oversampled Weyl-Heisenberg frames. Signal Process. 47 (1995) 239-245
23. Janssen A.J.E.M. Representations of Gabor frame operators. NATO Sci. Ser. II Math. Phys. Chem. vol. 33 (2001), Kluwer Acad. Publ., Dordrecht 73-101
24. Janssen A.J.E.M., and Strohmer T. Characterization and computation of canonical tight windows for Gabor frames. J. Fourier Anal. Appl. 8 (2002) 1-28
25. Nikolski N.K. Operators, Functions, and Systems: An Easy Reading, vol. 1 (2002), Amer. Math. Soc., Providence, RI
26. Rieffel M. Von Neumann algebras associated with pairs of lattices in Lie groups. Math. Ann. 257 (1981) 403-418
27. d). Canad. J. Math. 47 (1995) 1051-1094
28. d). Duke Math. J. 89 (1997) 237-282
29. Rudin W. Functional Analysis (1991), McGraw-Hill, New York
30. Zeevi Y. Multiwindow Gabor-type representations and signal representation by partial information. NATO Sci. Ser. II Math. Phys. Chem. vol. 33 (2001), Kluwer Acad. Publ., Dordrecht 173-199
31. Zibulski M., and Zeevi Y. Analysis of multiwindow Gabor-type schemes by frame methods. Appl. Comput. Harmon. Anal. 4 (1997) 188-221