A Characterization of Affine Dual Frames in L 2 (R n )

Applied and Computational Harmonic Analysis

Volumn 8, Issue 2, 2000, Pages 203-221

  Bownik, Marcin ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

Affine frame; quasiaffine frame; dual frame; wavelet

Indexed keywords

EID: 0000571056     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0284     Document Type: Editorial

References (22)

1. 2 . SIAM J. Math. Anal. 30:1999;678-697.
2. Bownik M. Tight frames of multidimensional wavelets. J. Fourier Anal. Appl. 3:1997;525-542.
3. M. Bownik, The construction of r-regular wavelets for arbitrary dilations, preprint, 1999.
4. A. Calogero, A characterization of wavelets on general lattices, J. Geom. Anal, to appear.
5. A. Calogero, and, G. Garrigós, A characterization of wavelet families arising from biorthogonal MRA's of multiplicity d, preprint, 1999.
6. Chui C. K., Shi X., Stöckler J. Affine frames, quasi-affine frames, and their duals. Adv. Comput. Math. 8:1998;1-17.
7. Dai X., Larson D. R., Speegle D. M. Wavelet sets in R n. J. Fourier Anal. Appl. 3:1997;451-456.
8. Frazier M., Garrigós G., Wang K., Weiss G. A characterization of functions that generate wavelet and related expansion. J. Fourier Anal. Appl. 3:1997;883-906.
9. Frazier M., Jawerth B. The φ-transform and applications to distribution spaces. Function Spaces and Applications, Lund, 1986. 1988;Springer Verlag, Berlin, New York. p. 223-246.
10. Frazier M., Jawerth B., Weiss G. Littlewood-Paley Theory and the Study of Function Spaces. 1991;Conference Board of the Mathematical Sciences, Washington, DC.
11. Gripenberg G. A necessary and sufficient condition for the existence of a father wavelet. Studia Math. 114:1995;207-226.
12. Gröchenig K., Ron A. Tight compactly supported wavelet frames of arbitrarily high smoothness. Proc. Amer. Math. Soc. 126:1998;1101-1107.
13. Han B. On dual wavelet tight frames. Appl. Comput. Harmon. Anal. 4:1997;380-413.
14. Hernández E., Weiss G. A First Course on Wavelets. Studies in Advanced Mathematics. 1996;CRC Press, Boca Raton, FL.
15. n ) and algebraic number theory. J. Number Theory. 57:1996;181-197.
16. n ) and algebraic number theory. J. Number Theory. 76:1999;330-336.
17. d ): the analysis of the analysis operator. J. Funct. Anal. 148:1997;408-447.
18. d ). II. Dual systems. J. Fourier Anal. Appl. 3:1997;617-637.
19. Soardi P., Weiland D. Single wavelets in n-dimensions. J. Fourier Anal. Appl. 4:1998;299-315.
20. Strichartz R. S. Wavelets and self-affine tilings. Constr. Approx. 9:1993;327-346.
21. Wang X. The Study of Wavelets from the Properties of their Fourier Transforms. 1995;Washington University.
22. Wojtaszczyk P. A Mathematical Introduction to Wavelets. 1997;Cambridge University Press, Cambridge, UK.