李云章 - 北京工业大学

个人简介

李云章，男,1966年生，教授,博士生导师, 基础数学学科博士点责任教授，美国《Math.Reviews》与德国《Zentralblatt MATH》评论员，国家科技奖励评审专家，北京市高等学校教学名师。1998年浙江大学数学系博士毕业，获博士学位，研究方向：小波分析；2004.2---2005.2访问加拿大麦克玛斯特大学（McMasterUniversity）数学与统计系；研究领域涉及小波分析与Gabor分析。主持完成国家自然科学基金、教育部留学回国人员科研启动基金、北京市自然科学基金、北京市优秀人才基金、北京市教委基金等多项国家级和省部级项目。关于多元小波乘子、子空间标架理论的研究工作受到了国内外同行的关注。研究成果发表在《Appl. Comput. Harmon. Anal.》、《J. Funct. Anal.》、《J. Fourier Anal. Appl.》、《J. Math. Phys.》、《Adv. Comput. Math.》、《J. Math. Anal. Appl.》、《J. Approx. Theory》、《Proc. Amer. Math. Soc.》、《Num. Func. Anal. Optim.》、《Acta Appl. Math.》、《Appl. Math. Comput.》、《Kyoto J. Math.》、《Kodai Math. J.》、《Appl. Anal.》、《Results Math.》、《Math. Methods Appl. Sci.》、《Int. J. Wavelets Multiresolut. Inf.Process.》、《Comm.Pure Appl. Anal.》、《Sci.China Math.》等期刊，其中SCI收录50余篇。指导的博士生获国家奖学金、北京工业大学优秀博士学位论文等奖项。

近期论文

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[1] Nonhomogeneousdual wavelet frames and mixed oblique extension principles in Sobolev spaces.Appl. Anal.97 (2018),no. 7, 1049–1073. . (with Jian-Ping Zhang) [2] Weak affinesuper bi-frames for reducing subspaces of L 2 (R,C L ) . Results Math.73(2018),no. 3, Art. 96, 17 pp. (with Yu Tian) [3] Partialaffine system-based frames and dual frames. Math. Methods Appl. Sci.40(2017),no. 18, 6927–6943. (withYu Tian) [4] Subspacedual super wavelet and Gabor frames. Sci. China Math.60(2017),no. 12, 2429–2446. (withYu Tian) [5] Weaknonhomogeneous wavelet bi-frames for reducing subspaces of Sobolev spaces.Numer. Funct. Anal. Optim.38(2017),no. 2, 181–204. (with Huifang Jia) [6] Weak Gaborbi-frames on periodic subsets of the real line. Int. J. Wavelets Multiresolut.Inf. Process.13(2015),no. 6, 1550046, 23 pp. (with Huifang Jia) [7] Weak(quasi-)affine bi-frames for reducing subspaces of L 2 (R d ) . Sci. ChinaMath.58(2015),no. 5, 1005–1022. (withHuifang Jia) [8] Vector-valuedGabor frames associated with periodic subsets of the real line. Appl. Math.Comput.253(2015), 102–115. (with Yan Zhang) [9] Acharacterization of dimension functions of a class of semi-orthogonal Parsevalframe wavelets. Math. Methods Appl. Sci.38(2015),no. 4, 751–764. (with Nan Lan) [10] Theconstruction of multivariate periodic wavelet bi-frames. J. Math. Anal. Appl.412 (2014), no. 2, 852–865. (withHui-Fang Jia) [11] Rationaltime-frequency multi-window subspace Gabor frames and their Gabor duals. Sci.China Math. 57 (2014), no. 1,145–160. (with Yan Zhang) [12] Rationaltime-frequency Gabor frames associated with periodic subsets of the real line.Int. J. Wavelets Multiresolut. Inf. Process. 12 (2014), no. 2, 1450013, 15 pp.(with Jean-Pierre Gabardo ) [13] Super Gaborframes on discrete periodic sets, Adv. Comput. Math. 38 (2013), no. 4, 763–799.(with Qiao-Fang Lian) [14] Rationaltime-frequency super Gabor frames and their duals, J. Math. Anal. Appl. 403(2013), no. 2, 619–632.(with Feng-YingZhou) [15] Latticetiling and density conditions for subspace Gabor frames. J. Funct. Anal. 265(2013), no. 7, 1170–1189. (withJean-Pierre Gabardo and Deguang Han ) [16] Theequivalence between seven classes of wavelet multipliers and arcwiseconnectivity they induce. J. Fourier Anal. Appl. 19 (2013), no. 5, 1060–1077.(with Yan-Qin Xue) [17] Superoblique Gabor duals of super Gabor frames on discrete periodic sets,Num. Func. Anal. Optim., 34(2013), no. 3,284–322. (with Qiao-Fang Lian) [18] Rationaltime-frequency vector-valued subspace Gabor frames and Balian-Low theorem, Int.J. Wavelets Multiresolut. Inf. Process., 11(2013), no.1, 1350013, 23pp. (withYan Zhang) [19] Generalizedmultiresolution structures in reducing subspaces of $L^2(Bbb R^d)$, Sci. ChinaMath., 56(2013), 619–638. (with Feng-Ying Zhou) [20] Anembedding theorem on reducing subspace frame multiresolution analysis. KodaiMath. J. 35 (2012), no. 1, 157–172. (with Lin Zhang) [21] Gaborfamilies in $l^2(Bbb Z^d)$, Kyoto J. Math. 52 (2012), no. 1, 179–204. (withQiao-Fang Lian) [22] Thecharacterization of a class of multivariate MRA and semi-orthogonalParsevalframe wavelets,Appl. Math. Comput.,217(2011), no. 22, 9151–9164 .(with Feng-Ying Zhou) [23] Gabor framesets for subspaces, Adv. Comput. Math, 34(2011), no. 4, 391–411. (withQiao-Fang Lian) [24] GMRA-basedconstruction of framelets in reducing subspaces of $L^2(Bbb R^d)$, Int. J.Wavelets Multiresolut. Inf. Process., 9 (2011), no. 2, 237–268.(with Feng-Ying Zhou) [25]Multi-window Gabor frames and oblique Gabor duals on discrete periodic sets，Sci.China Math., 54(2011), no. 5, 987–1010.(with Qiao-Fang Lian) [26]Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of$L^2(Bbb R^d)$,Kyoto J. Math., 50 (2010), no. 1, 83–99.(with Feng-Ying Zhou) [27]Gabor systems on discrete periodic sets. Sci.China Ser. A 52 (2009), no. 8, 1639-1660. (with Qiao-Fang Lian) [28] Densityresults for Gabor systems associated with periodic subsets of the real line. J.Approx. Theory 157 (2009),no. 2, 172--192. (with Jean-Pierre Gabardo) [29] The dualsof Gabor frames on discrete periodic sets. J. Math. Phys. 50 (2009), no. 1,013534, 22 pp.(with Qiao-Fang Lian) [30] Tight Gaborsets on discrete periodic sets. Acta Appl. Math. 107(2009), no. 1-3, 105--119. (with Qiao-FangLian) [31] Holes inthe spectrum of functions generating affine systems. Proc. Amer. Math. Soc.,135(2007), no. 6, 1775--1784 (with Jean-Pierre Gabardo) [32] Reducingsubspace frame multiresolution analysis and frame wavelets. Commun. Pure Appl.Anal. 6 (2007), no. 3, 741--756. (with Qiao-Fang Lian) [33] On theconstruction of a class of bidimensional nonseparable compactly supported wavelets.Proc. Amer. Math. Soc.133 (2005), no. 12, 3505—3513 [34] A note onGabor orthonormal bases. Proc. Amer. Math. Soc. 133 (2005), no. 8,2419-2428 [35] On theholes of a class of bidimensional nonseparable wavelets. J. Approx. Theory, 125(2003), no. 2, 151--168. [36] On a classof bidimensional nonseparable wavelet multipliers. J. Math. Anal. Appl., 270(2002), no. 2, 543--560. [37] Extension principles for affine dual frames in reducing subspaces,Appl. Comput. Harmon. Anal., (2017), https://doi.org/10.1016/j.acha.2017.11.006