Unitary systems and wavelet sets

Applied and Numerical Harmonic Analysis

Volumn , Issue 9783764377779, 2007, Pages 143-171

  Larson, David R ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Frame; Unitary system; Wavelet; Wavelet set

Indexed keywords

EID: 85010203809     PISSN: 22965009     EISSN: 22965017     Source Type: Book Series    
DOI: 10.1007/978-3-7643-7778-6_14     Document Type: Chapter

References (26)

1. E. A. Azoff, E. J. Ionascu, D. R. Larson, and C. M. Pearcy, Direct Paths of Wavelets. Houston J. Math. 29 (2003), no. 3, 737-756.
2. L. Baggett, H. Medina, and K. Merrill, Generalized Multi-resolution Analyses and a Construction Procedure for all Wavelet Sets in R n. J. Fourier Anal. Appl. 5 (1999).
3. J. J. Benedetto and M. Leon, The Construction of Single Wavelets in D-dimensions. J. Geom. Anal. 11 (2001), no. 1, 1-15.
4. X. Dai, Y. Diao, Q. Gu and D. Han, Wavelets with Frame Multiresolution Analysis. J. Fourier Analysis and Applications 9 (2003), 39-48.
5. X. Dai and D. Larson, Wandering Vectors for Unitary Systems and Orthogonal Wavelets. Mem. Amer. Math. Soc. 134 (1998).
6. X. Dai, D. Larson and D. Speegle, Wavelet Sets in R n. J. Fourier Anal. Appl. 3 (1997), no. 4, 451-456.
7. X. Dai, D. Larson, and D. Speegle, Wavelet Sets in R n — II. Contemp. Math 216 (1998), 15-40.
8. I. Daubechies, Ten Lectures on Wavelets. SIAM Philadelphia, PA, 1992.
9. X. Fang and X. Wang, Construction of Minimally-supported Frequencies Wavelets. J. Fourier Anal. Appl. 2 (1996), 315-327.
10. T. N. T. Goodman, S. L. Lee and W. S. Tang, Wavelets in Wandering Subspaces. Transactions AMS 338 (1993), 639-654.
11. Q. Gu, On Interpolation Families of Wavelet Sets. Proc. Amer. Math. Soc. 128 (2000), 2973-2979.
12. D. Han, Wandering Vectors for Irrational Rotation Unitary Systems. Transactions AMS 350 (1998), 309-320.
13. D. Han, J-P. Gabardo, and D. R. Larson, Gabor Frames and Operator Algebras. Wavelet Appl. in Signal and Image Proc., Proc. SPIE 4119 (2000), 337-345.
14. D. Han and D. R. Larson, Frames, Bases and Group Representations. Memoirs AMS 697(2000).
15. D. Han and D. R. Larson, Wandering Vector Multipliers for Unitary Groups. Transactions AMS 353 (2001), 3347-3370.
16. C. Heil, P. E. T. Jorgensen, and D. R. Larson (eds.), Wavelets, Frames and Operator Theory, Contemp. Math., 345. AMS, Providence, RI, 2004, College Park, MD, Jan. 15-21, 2003.
17. E. Hernandez, X. Wang and G. Weiss, Smoothing Minimally Supported Frequency (MSF) Wavelets: Part I. J. Four. Anal. Appl. 2 (1996), 329-340.
18. E. Ionascu, D. Larson, and C. Pearcy, On the Unitary Systems Affiliated with Orthonormal Wavelet Theory in n-dimensions. J. Funct. Anal. 157 (1998), no. 2, 413-431.
19. R. Kadison and J. Ringrose, Fundamentals of the Theory of Opera tor Algebras, Vol. I and II. Academic Press, Inc. 1983 and 1985.
20. K. Kornelson and D. Larson, Rank-one Decomposition of Operators and Construction of Frames. Wavelets, Frames, and Operator Theory, Contemp. Math., 345. AMS, 2004, pp. 203-214.
21. D. R. Larson, Von Neumann Algebras and Wavelets. Operator Algebras and Applications (Samos, 1996), 267-312. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997.
22. D. R. Larson, Frames and Wavelets from an Operator-theoretic Point of View, Operator Algebras and Operator Theory (Shanghai, 1997), 201-218. Contemp. Math., 228, AMS, Providence, RI, 1998.
23. D. R. Larson, E. Schulz, D. Speegle, and K. Taylor, Explicit Cross Sections of Singly Generated Group Actions, to appear.
24. D. R. Larson, W. S. Tang, and E. Weber, Multiwavelets Associated with Countable Groups of Unitary Operators in Hilbert Spaces. Int. J. Pure Appl. Math. 6 (2003), no. 2, 123-144.
25. D. Speegle, The s-elementary Wavelets are Path-connected. Proc. Amer. Math. Soc. 132(2004), 2567-2575
26. Wutam Consortium, Basic Properties of Wavelets. J. Four. Anal. Appl. 4 (1998), 575-594