波包Parseval框架的刻画及应用

吴国昌, 曹怀信, 鲁大勇

数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 91-102.

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数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 91-102. DOI: 10.12386/A2015sxxb0009
论文

波包Parseval框架的刻画及应用

    吴国昌1,2, 曹怀信1, 鲁大勇3
作者信息 +

The Characterization of Wave Packet Parseval Frames and Its Application

    Guo Chang WU1,2, Huai Xin CAO1, Da Yong LU3
Author information +
文章历史 +

摘要

给出波包Parseval框架的一个频域刻画,得到了作为推论存在的结果,从而获得波包框架乘子的性质和充分条件.

Abstract

We provide a characterization of wave packet Parseval frames from their Fourier transforms, which deduces some existing results as e corollaries. Furthermore, some properties and a sufficient condition of wave packet frame multipliers are obtained.

关键词

波包系统 / Parseval框架 / 波包框架乘子

Key words

wave packet system / Parseval frame / wave packet frame multiplier

引用本文

导出引用
吴国昌, 曹怀信, 鲁大勇. 波包Parseval框架的刻画及应用. 数学学报, 2015, 58(1): 91-102 https://doi.org/10.12386/A2015sxxb0009
Guo Chang WU, Huai Xin CAO, Da Yong LU. The Characterization of Wave Packet Parseval Frames and Its Application. Acta Mathematica Sinica, Chinese Series, 2015, 58(1): 91-102 https://doi.org/10.12386/A2015sxxb0009

参考文献

[1] Casazza P., Christensen O., Weyl-Heisenberg frames for subspaces of L2(R), Proc. Amer. Math. Soc., 2001, 129: 145-154.

[2] Casazza P., Kovaěvi? J., Equal-norm tight frames with erasures, Adv. Comput. Math., 2003, 18: 387-430.

[3] Christensen O., An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2002.

[4] Christensen O., Rahimi A., Frame properties of wave packet systems in L2(Rd), Adv. Comput. Math., 2008, 29: 101-111.

[5] Chui C., Shi X., Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 1993, 24: 263-277.

[6] Cordoba A., Fefferman C., Wave packets and Fourier integral operators, Comm. Partial Differrential Equations, 1978, 3: 979-1005.

[7] Czaja W., Characterizations of gabor systems via the Fourier transform, Collect. Math., 2000, 51(2): 205- 224.

[8] Czaja W., Kutyniok G., Speegle D., The Geometry of sets of prameters of wave packets, Appl. Comput. Harmon. Anal., 2006, 20: 108-125.

[9] Daubechies I., Ten Lectures on Wavelets, in: CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, SIAM, Philadelphia, 1992.

[10] Daubechies I., The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 1990, 36: 961-1005.

[11] Daubechies I., Groddmann A., Mayer Y., Painless nonorthogonal expansions, J. Math. Phys., 1986, 27: 1271-1283.

[12] Duffin R., Schaeffer A., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 1952, 72: 341-366.

[13] Frazier M., Garrigos G., Wang K., Weiss G., A characterization of functions that generate wavelet and related expansions, J. Fourier Anal. Appl., 1997, 3: 883-906.

[14] Gabor D., Thoery of communications, J. Inst. Elec. Engrg., 1946, 93, 429-457.

[15] Goyal V., Kovaěvi? J., Kelner J., Quantized frames expansions with erasures, Appl. Comput. Harmon. Anal., 2001, 10: 203-233.

[16] Hassibi B., Hochwald B., Shokrollahi A., Sweldens W., Representation theory for high-rate multiple-antenna code design, IEEE Trans. Inform. Theory, 2001, 47: 2335-2367.

[17] Hernandez E., Labate D., Weiss G., Wilson E., Oversampling, quasi affine frames and wave packets, Appl. Comput. Harmon. Anal., 2004, 16: 111-147.

[18] Huang Y. D., Suin N., The Characterizations of A-Parseval Frame Wavelet, Acta Mathematica Sinica, Chinese Series, 2011, 54(5): 767-790.

[19] Paluszyński M., Šiki? H., Weiss G., Xiao S., Generalized low pass filters and MRA frame wavelets, J. Geom. Anal., 2001, 11(2): 311-342.

[20] Lacey M., Thiele C., Lp estimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. of Math., 1997, 146: 693-724.

[21] Lacey M., Thiele C., On Calderón's conjecture, Ann. of Math., 1999, 149: 475-496.

[22] Labate D., Weiss G., Wilson E., An approach to the study of wave packet systems, Contemp. Math., Wavelets, Frames and Operator Theory, 2004, 345: 215-235.

[23] Li D., Shi X., A sufficient condition for affine frames with matrix dilation, Anal. Theory Appl., 2009, 25: 66-174.

[24] Li D., Shi X., Tight multiwavelet frames with different matrix dilations and matrix translations, Numer. Funct. Anal. Optimiz., 2009, 31(7): 798-813.

[25] Li D., Wu G., Two sufficient conditions in frequency domain for Gabor frames, Applied Mathematics Letters, 2011, 24(4): 506-511.

[26] Li Y., Yang S., Explicit construction of symmetric orthogonal wavelet frames in L2(Rs), J. Approx. Theory, 2010, 162(5): 891-909.

[27] Lian Q., Li Y., Gabor frame sets for subspaces, Adv. Comput. Math., 2011, 34(4): 391-411.

[28] Lü D. Y., Fan Q. B., Gabor frames generated by multiple generators, Sci. China, Ser. A, 2010, 40(7): 693-708.

[29] Shi X., Chen F., Necessary conditions for Gabor frames, Sci. China, Ser. A, 2007, 50(2): 276-284.

[30] The Wutam Consortium, Basic properties of wavelets, J. Fourier Anal. Appl., 1998, 4(4): 575-594.

基金

国家自然科学基金项目资助(11371012);河南省科技厅基础与前沿资助项目(122300410381)和河南省教育厅科学技术研究重点项目(13A110072, 14A110006)

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