华北电力大学“前沿&创新”学术论坛第305期:Isomorphism in wavelets

【讲座题目】Isomorphism in wavelets

【讲座时间】2019年5月22日(星期15:00-16:00

【讲座地点】主C636

【主 人】戴兴德

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【主讲人简介】

戴教授于美国德克萨斯A&M大学获得博士学位,现为美国北卡罗来纳夏洛特分校终身教授。戴教授是国际著名的泛函分析与小波分析专家。戴教授和导师D. Larson教授于上世纪90年代成功地将泛函分析算子代数与调和分析框架小波理论相结合,开创了这两个领域交叉研究的新方向,该理论具有着广泛的理论和应用价值,是国际研究的热点领域,被国际上称为Dai-Larson理论。戴教授的开创性的研究成果(高倍引论文)为 Wandering vectors for unitary systems and orthogonal wavelets (Mem. Amer. Math. Soc.134 (1998), no. 640, viii+68 pp);  Wavelet sets in Rn ( J. Fourier Anal. Appl.3 (1997), no. 4, 451–456);  Wavelet sets in rn II (Amer. Math. Soc., Providence, RI, 1998) 。

【讲座内容简介】

Two scaling functions J(A) and J(B) for Parseval frame wavelets are algebraically isomorphic, , if they have matching solutions to their (reduced) isomorphic systems of equations.

Let A and B be d×d and s×s dyadic expansive integral matrices with d, s1  respectively and let J(A) be a scaling function associated with matrix A and generated by a finite solution. Then there always exists a scaling function J(B)  associated with matrix B such that J(B)  is algebraically isomorphic to J(A).

An example shows that the assumption on the finiteness of the solutions can not be removed.