仿射Bessel序列的判别

王玮, 施咸亮

数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 673-678.

PDF(308 KB)
PDF(308 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 673-678. DOI: 10.12386/A2015sxxb0068
论文

仿射Bessel序列的判别

    王玮1, 施咸亮2
作者信息 +

Criterion on Affine Bessel Sequences

    Wei WANG1, Xian Liang SHI2
Author information +
文章历史 +

摘要

通过引进Bessel控制函数,并对它的充分性和必要性作研究,建立了对仿射Bessel序列的新的判别法.最后提出几个未解决的问题.

Abstract

By introducing Bessel control functions, and studying its necessary conditions and sufficient conditions, a new criterion for affine Bessel sequences with control functions is established. Furthermore, some open questions are posed.

关键词

Fourier变换 / Bessel序列 / 框架

Key words

Fourier transform / Bessel sequences / frame

引用本文

导出引用
王玮, 施咸亮. 仿射Bessel序列的判别. 数学学报, 2015, 58(4): 673-678 https://doi.org/10.12386/A2015sxxb0068
Wei WANG, Xian Liang SHI. Criterion on Affine Bessel Sequences. Acta Mathematica Sinica, Chinese Series, 2015, 58(4): 673-678 https://doi.org/10.12386/A2015sxxb0068

参考文献

[1] Chui C. K., Shi X. L., Bessel sequences and affine frames, Appl. Comp. Harmon. Anal., 1993, 1: 29-49.

[2] Chui C. K., Shi X. L., On a Littlewood-Paley identity and characterization of wavelet, Math. Anal. Appl., 1993, 177: 608-626.

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

[4] Li D. F., Shi X. L., A sufficient condition for affine frames with matrix dilations, Anal. Theory Appl., 2009, 25(2): 166-174.

[5] Li D. F., Shi X. L., Tight multiwavelet frames with different matrix dilations and matrix translations, Numer. Func. Anal. Opt., 2010, 31(7): 798-813.

[6] Shi X. L., Shi Q. L., A new criterion on affine frames, Chin. Ann. Math. Ser. A, 2005, 26(2): 257-262.

基金

国家自然科学基金资助项目(11071065, 11171306); 数学天元青年基金资助项目(11426221);湖南省自然科学基金资助项目(13JJ4088)

PDF(308 KB)

Accesses

Citation

Detail

段落导航
相关文章

/