Oblique multiwavelets in Hilbert spaces

Tang, Wai-Shing

doi:10.1090/S0002-9939-99-05432-5

Oblique multiwavelets in Hilbert spaces
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Proc. Amer. Math. Soc. 128 (2000), 2017-2031 Request permission

Abstract:

In this paper, we elucidate the relationship between two consecutive levels of a multiresolution in the general setting of a Hilbert space. We first prove a result on an extendability problem and then derive, as a consequence, characterizations of oblique multiwavelets in a Hilbert space.

References

Akram Aldroubi, Oblique and hierarchical multiwavelet bases, Appl. Comput. Harmon. Anal. 4 (1997), no. 3, 231–263. MR 1454403, DOI 10.1006/acha.1997.0211
Akram Aldroubi and Manos Papadakis, Characterization and parameterization of multiwavelet bases, Wavelets, multiwavelets, and their applications (San Diego, CA, 1997) Contemp. Math., vol. 216, Amer. Math. Soc., Providence, RI, 1998, pp. 97–116. MR 1614716, DOI 10.1090/conm/216/02967
A. Cohen, Ingrid Daubechies, and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), no. 5, 485–560. MR 1162365, DOI 10.1002/cpa.3160450502
T. N. T. Goodman, S. L. Lee, and W. S. Tang, Wavelets in wandering subspaces, Trans. Amer. Math. Soc. 338 (1993), no. 2, 639–654. MR 1117215, DOI 10.1090/S0002-9947-1993-1117215-0
T. N. T. Goodman, S. L. Lee, and W. S. Tang, Wavelet bases for a set of commuting unitary operators, Adv. Comput. Math. 1 (1993), no. 1, 109–126. MR 1230253, DOI 10.1007/BF02070823
Rong Qing Jia and Zuowei Shen, Multiresolution and wavelets, Proc. Edinburgh Math. Soc. (2) 37 (1994), no. 2, 271–300. MR 1280683, DOI 10.1017/S0013091500006076
S. L. Lee, H. H. Tan, and W. S. Tang, Wavelet bases for a unitary operator, Proc. Edinburgh Math. Soc. (2) 38 (1995), no. 2, 233–260. MR 1335872, DOI 10.1017/S0013091500019064
S. L. Lee and W. S. Tang, Characterizations of wavelet bases and frames in Hilbert spaces, Proc. SPIE. 3169 (1997), 282–290.
M. A. Naĭmark, Normed rings, Reprinting of the revised English edition, Wolters-Noordhoff Publishing, Groningen, 1970. Translated from the first Russian edition by Leo F. Boron. MR 0355601
W. S. Tang, Oblique projections, biorthogonal Riesz bases and multiwavelets in Hilbert spaces, Proc. Amer. Math. Soc. (to appear).
Robert M. Young, An introduction to nonharmonic Fourier series, Pure and Applied Mathematics, vol. 93, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 591684