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
Time
Wednesday, July 10, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
Let
that this system is hereditarily complete or admits spectral synthesis if any vector in
can be approximated in the norm by linear combinations of partial sums of the Fourier
series with respect to
minimal system of exponentials in
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).
that this system is hereditarily complete or admits spectral synthesis if any vector in
can be approximated in the norm by linear combinations of partial sums of the Fourier
series with respect to
minimal system of exponentials in
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.