【讲座题目】Isomorphism in wavelets

【讲座时间】2019年5月22日（星期三）15:00-16：00

【讲座地点】北京校部主楼C636

【主 讲 人】戴兴德 教授

【主讲人简介】

戴兴德，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，他和导师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) 。

【内容简介】

Two scaling functions and 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, s≥1  respectively and let   be a scaling function associated with matrix A and generated by a finite solution. Then there always exists a scaling function   associated with matrix B such that    is algebraically isomorphic to  .

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