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About
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Visit
People
Management
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Postdocs
Visiting Scholars
Staff
Research
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Courses
Seminars
Join Us
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Moscow-Beijing topology seminar Spectral synthesis for systems of exponentials and reproducing kernels
Spectral synthesis for systems of exponentials and reproducing kernels
Organizers
Vassily Manturov , Shiquan Ren , Zhe Yan Wan
Speaker
Yurii Belov
Time
Wednesday, July 10, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580 (141592)
Abstract
Let xn be a complete and minimal system of vectors in a Hilbert space H. We say
that this system is hereditarily complete or admits spectral synthesis if any vector in H
can be approximated in the norm by linear combinations of partial sums of the Fourier
series with respect to xn. It was a long-standing problem whether any complete and
minimal system of exponentials in L2(−a,a) admits spectral synthesis. Several years ago
A. Baranov, A. Borichev and myself managed to give a negative answer to this question which implies,
in particular, that there exist non-harmonic Fourier series which do not admit a linear
summation method. We also showed that any exponential system admits the
synthesis up to a one-dimensional defect. Apart from this, I will discuss related problems
for systems of reproducing kernels in Hilbert spaces of entire functions. In particular,
I will talk about a counterexample to the Newman-Shapiro conjecture posed in 1966
(joint work with A. Borichev).
Speaker Intro
Yurii Belov is a professor at St. Petersburg State University and vice-chair of educational program "Mathematics" headed by Stanislav Smirnov. He got his PhD degree in 2007 (Norwegian University of Science and Technology) and Dr.Sci. degree in 2016 (St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Russia). He was a postdoc at Norwegian University of Science and Technology. Yurii Belov was awarded by the St. Petersburg Mathematical Society the prize for young mathematicians and won the "Young Russian Mathematics" contest (twice). In 2016 he got the L. Euler award from the Government of St. Petersburg.
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