Title: Fourier analysis on finite abelian groups and uncertainty principles
Time：     14:00-15:00, July16 Tuesday,2019
Location:   Room 1202, Science Building B
Lecturer：Prof. Xiang Qing  University of Delaware 

Abstract:
Let $G$ be a finite abelian group. If $f: G/rightarrow {/bf C}$  is a nonzero function with Fourier transform $/hf$, the Donoho-Stark uncertainty principle states that $|/supp(f)||/supp(/hf)|/geq |G|$. The purpose of this talk is twofold. First, we present the shift bound for abelian codes with a streamlined proof. Second, we use the shifting technique to prove a generalization and a sharpening of the Donoho-Stark uncertainty principle. In particular, the sharpened uncertainty principle states, with notation above, that $$|/supp(f)||/supp(/hf)|/geq |G|+|/supp(f)|-|H(/supp(f))|,$$ where $H(/supp(f))$ is the stabilizer of $/supp(f)$ in $G$.

Introduction of Lectuer:
Xiang Qing, who received a doctorate from Ohio State University in 1995, is now a professor at the University of Delaware. The main research directions are combinatorial design, finite geometry, coding and additive combination. At present, he is the editor in chief of the electronic journal of combinatorics, an international authoritative journal in combinatorial mathematics, and the editorial board member of SCI journals designs, codes and cryptography and Journal of combinatorial designs. He was awarded Kirkman medal by the International Association of combinatorics and its applications. More than 80 academic papers have been published in J. combin. Theory Ser. A, J. combin. Theory Ser. B, combinatorial, trans. Amer. Math. SOC, IEEE Trans. Information. Theory and other important international journals. Presided over and completed more than 10 scientific research projects such as National Natural Science Foundation of the United States and national security administration of the United States. He has made more than 50 conference reports or invited reports at international academic conferences.