A violation of the uncertainty principle: indicator functions with thin spectrum and uniformly bounded partial Fourier integrals

• 主讲人：Sergey Kislyakov (St.Petersburg Department of Steklov Mathematical Institute)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-05-19 20:00 - 2022-05-19 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/872A119E054BC012A4A81977B8AA410E
Valid Until: 2026-06-30 23:59

 

Abstract: Given a set $a$ of finite measure on the real line, it is possible to find a set $b$ with the properties mentioned in the title and differing from $a$ as little as we want in the sense of measure. There is an analog of this claim for more or less general LCA groups. The discussion will be prefaced with a short survey of various results about conditions that may or may not be fulfilled simultaneously for a function and its Fourier transform. This is a joint work with P.Perstneva.

 

Bio: Sergey Vitalievich Kislyakov is one of the best Russian experts in Harmonic Analysis, Functional Analysis, Interpolation theory, Fourier Analysis and many other related fields, having obtained a great deal of outstanding results in these areas. Besides, he is the author of several books that are extremely popular both among students and mature researchers.  Prof. Kislyakov is a Doctor of Mathematics, an Academician of the Russian Academy of Sciences (since 2016), and the Chief Editor of the "Algebra and Analysis" journal. He was Director of the Saint Petersburg Department of Steklov Mathematical Institute.