BIMSA >
Moscow-Beijing topology seminar
Spectral synthesis for systems of exponentials and reproducing kernels
Spectral synthesis for systems of exponentials and reproducing kernels
组织者
Vassily Manturov
, 任世全
,
万喆彦
演讲者
时间
2024年07月10日 15:30 至 17:00
地点
A3-2-301
线上
Zoom 831 5020 0580
(141592)
摘要
Let $x_n$ 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 $x_n$. It was a long-standing problem whether any complete and
minimal system of exponentials in $L^2(-a,a)$ 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).
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 $x_n$. It was a long-standing problem whether any complete and
minimal system of exponentials in $L^2(-a,a)$ 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).
演讲者介绍
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.