Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn)

Journal of Fourier Analysis and Applications

Volumn 9, Issue 2, 2003, Pages 101-116

  Packer, Judith A ^a,b   Rieffel, Marc A ^c  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF COLORADO   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

C* algebras; Filters; Finitely generated projective modules; Hubert C* module; K theory; Wavelets

Indexed keywords

EID: 0037652075     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-003-0010-4     Document Type: Review

References (34)

1. Ashino, R. and Kametani, M. (1997). A lemma on matrices and a construction of multi-wavelets, Math. Japon., 45, 267-287.
2. Baggett, L., Carey, A., Moran, W., and Ohring, P. (1995). General existence theorems for orthonormal wavelets, an abstract approach, Publ. Res. Inst. Math. Sci., 31, 95-111.
3. n, in The Functional and Harmonic Analysis of Wavelets and Frames, 17-27, Baggett, L. and Larson, D., Eds., Proceedings of AMS Special Session on the Functional and Harmonic Analysis, January 13-14, 1999, San Antonio, TX, American Mathematical Society, Providence, RI.
4. 2, J. Approx. Theory, 116, 49-75.
5. Blackadar, B. (1998). K-Theory for Operator Algebras, second ed., Mathematical Science Research Institute Publications, Vol. 5, Cambridge University Press, Cambridge, UK.
6. Bratteli, O. and Jorgensen, P. (2002). Wavelet filters and infinite-dimensional unitary groups, in Wavelet Analysis and Applications (Guangzhou, 1999), 35-65, American Mathematical Society, Providence, RI, arXiv:math.FA/0001171.
7. Casazza, P.G. (1999). Modern tools for Weyl-Heisenberg (Gabor) frames, preprint.
8. Frank, M. and Larson, D.R. (1999). A module frame concept for Hubert C*-modules, in The Functional and Harmonic Analysis of Wavelets and Frames, 201-233, Baggett, L. and Larson, D., Eds., Proceedings of AMS Special Session on the Functional and Harmonic Analysis, January 13-14,1999, San Antonio, TX, American Mathematical Society, Providence, RI.
9. Gröchenig, K. (1987). Analyze multi-échelles et bases d'ondelettes, C. R. Acad. Sci. Paris Sér. 1 Math., 305, 13-15.
10. Gröchenig, K. and Ron, A. (1998). Tight compactly supported wavelet frames of arbitrarily high smoothness, Proc. Am. Math. Soc., 126, 1101-1107.
11. Husemoller, D. (1974). Fibre Bundles, second ed., Springer-Verlag, New York, Heidelberg, Berlin.
12. Jia, R.-Q. and Micchelli, C.A. (1991). Using the refinement equations for the construction of pre-wavelets, II. Powers of two, in Curves and Surfaces (Chamonix-Mont-Blanc, 1990), 209-246, Academic Press, Boston, MA.
13. Jia, R.-Q. and Micchelli, C.A. (1992). Using the refinement equation for the construction of pre-wavelets, V. Extensibility of trigonometric polynomials, Computing, 48, 61-72.
14. Lance, E.G. (1995). Hubert C*-Modules: A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge.
15. Maunder, C.R.F. (1980). Algebraic Topology, Cambridge University Press, Cambridge-New York.
16. Meyer, Y. (1988). Ondelettes, fonctions splines et analyses graduées, Rend. Sem. Mat. Univ. Politec. Torino, 45, 1-42.
17. Meyer, Y. (1992). Wavelets and Operators, Cambridge University Press, Cambridge-New York.
18. Packer, J. and Rieffel, M. Projective module wavelet frames over continuous functions on tori, in preparation.
19. Raeburn, I. and Williams, D.P. (1998). Morita equivalence and continuous-trace C*-algebras, Mathematical Surveys and Monographs, 60. American Mathematical Society, Providence, RI.
20. Rieffel, M.A. (1974). Induced representations of C*-algebras, Adv. Math., 13, 176-257.
21. Rieffel, M.A. (1981). C*-algebras associated with irrational rotations, Pacific J. Math., 93,415-429.
22. Rieffel, M.A. (1982). Applications of strong Morita equivalence to transformation group algebras, in Operator Algebras and Applications, Proceedings of Symposia in Pure Mathematics, Vol. 38, part 1, 299-310, Kadison, R.V., Ed., American Mathematical Society, Providence, RI.
23. Rieffel, M.A. (1987). The homotopy groups of the unitary groups of noncommutative tori, J. Operator Theory, 17, 237-254.
24. Rieffel, M.A. (1988). Projective modules over higher dimensional non-commutative tori, Canad. J, Math., 40, 257-338.
25. Rieffel, M.A. (1997). Multiwavelets and operator algebras, talk at a special session, joint mathematics meeting, San Diego, January 8-11,1997, cf. Abstracts Am. Math. Soc., 18, 107, 918-46-722.
26. d): the analysis of the analysis operator, J. Funct. Anal., 148, 408-447.
27. Rosenberg, J. (1994). Algebraic K-Theory and its Applications, Springer-Verlag, New York.
28. Selick, P. (1997). Introduction to homotopy theory, Fields Institute Monographs, 9, American Mathematical Society, Providence, RI.
29. Steenrod, N. (1951). The Topology of Fibre Bundles, Princeton University Press.
30. Strichartz, R. (1994). Construction of orthonormal wavelets, in Wavelets: Mathematics and Applications, 23-50, Benedetto, J. and Frazier, M., Eds., CRC Press, Boca Raton, FL.
31. Spanier, E. (1966). Algebraic Topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London.
32. Watatani, Y. (1990). Index for C*-subalgebras, Mem. Am. Math. Soc., 424, American Mathematical Society, Providence, RI.
33. Wegge-Olsen, N.E. (1993). K-Theory and C*-Algebras. A Friendly Approach, The Clarendon Press, Oxford University Press, New York.
34. Wojtaszczyk, P. (1997). A Mathematical Introduction to Wavelets, London Mathematical Society Student Texts 37, Cambridge University Press, Cambridge, UK.