Frames and single wavelets for unitary groups

Canadian Journal of Mathematics

Volumn 54, Issue 3, 2002, Pages 634-647

  Weber, Eric ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Frame; Multiresolution analysis; Unitary group representation; Wavelet

Indexed keywords

EID: 0035997731     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2002-023-3     Document Type: Article

References (18)

1. L. Baggett, A. Carey, W. Moran and P. Ohring, General Existence Theorems for Orthonormal Wavelets, An Abstract Approach. Publ. Res. Inst. Math. Sci. (1) 31(1995), 95-111.
2. L. Baggett, J. Courter and K. Merrill, Construction of Wavelets from Generalized Conjugate Mirror Filters. Preprint, 2000.
3. n. J. Fourier Anal. Appl. (6) 5(1999), 563-573.
4. J. Benedetto and S. Li, The Theory of Multiresolution Analysis Frames and Applications to Filter Banks. Appl. Comput. Harmon. Anal. (4) 5(1998), 389-427.
5. P. Casazza, The Art of Frame Theory. Taiwanese J. Math. (2) 4(2000), 129-201.
6. J. Courter, Construction of Dilation-d Orthonormal Wavelets. Ph.D. thesis, University of Colorado, Boulder, 1999.
7. I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. (7) 41(1988), 909-996.
8. P. Halmos, Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea, New York, 1957.
9. D. Han and D. Larson, Frames, Bases and Group Representations. Mem. Amer. Math. Soc. (697) 147(2000).
10. D. Han, D. Larson, M. Papadakis and T. Stavropoulos, Multiresolution Analyses of Abstract Hilbert Spaces and Wandering Subspaces. In: The Functional and Harmonic Analysis of Wavelets and Frames, Contemp. Math. 247(1999), 259-284.
11. E. Hernandez and G. Weiss, An Introduction to Wavelets. CRC Press, Boca Raton, 1998.
12. S. Lee, H. Tan and W. Tang, Wavelet Bases for a Unitary Operator. Proc. Edinburgh Math. Soc. 38(1995), 233-260.
13. 2 (ℝR). Trans. Amer. Math. Soc. (1) 315(1989), 69-87.
14. M. Papadakis, Generalized Frame MRAs of Abstract Hilbert Spaces. Preprint, 2000.
15. _, On the dimension function of a wavelet. Proc. Amer. Math. Soc. (7) 128(2000), 2043-2049.
16. J. Robertson, On Wandering Subspaces for Unitary Operators. Proc. Amer. Math. Soc. 16(1965), 233-236.
17. S. Schaffer, Generalized Multiresolution Analyses and Applications of their Multiplicity Functions to Wavelets. Ph.D. thesis, University of Colorado, Boulder, 2000.
18. E. Weber, On the translation invariance of wavelet subspaces. J. Fourier Anal. Appl. (5) 6(2000), 551-558.