SHANNON SAMPLING ON MANIFOLDS AND GRAPHS

Seminar
Speaker
Prof. Isaac Pesenson, Temple University, Philadelphia, USA
Date
20/05/2019 - 15:40 - 14:00Add to Calendar 2019-05-20 14:00:00 2019-05-20 15:40:00 SHANNON SAMPLING ON MANIFOLDS AND GRAPHS One of the most interesting properties of the so called bandlimited functions (=Palley-Wiener functions), i. e. functions whose Fourier transform has compact support, is that they are uniquely determined by their values on some countable sets of points and can be reconstructed from such values in a stable way. The sampling problem for band limited functions had attracted attention of many mathematicians. The mathematical theory of reconstruction of band limited functions from discrete sets of samples was introduced to the world of signal analysis and information theory by Shannon. Later the concept of bandlimitedness and the Sampling Theorem became the theoretical foundation of many branches of the information theory. In the talk I will show how these ideas can be extended to the setting of Riemannian manifolds and combinatorial graphs. It is an active field of research which found numerous applications in machine learning, astrophysics, and statistics. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

One of the most interesting properties of the so called bandlimited functions
(=Palley-Wiener functions), i. e. functions whose Fourier transform has compact
support, is that they are uniquely determined by their values on some countable sets
of points and can be reconstructed from such values in a stable way. The sampling
problem for band limited functions had attracted attention of many mathematicians.
The mathematical theory of reconstruction of band limited functions from discrete
sets of samples was introduced to the world of signal analysis and information
theory by Shannon. Later the concept of bandlimitedness and the Sampling Theorem
became the theoretical foundation of many branches of the information theory.
In the talk I will show how these ideas can be extended to the setting of Riemannian
manifolds and combinatorial graphs. It is an active field of research which
found numerous applications in machine learning, astrophysics, and statistics.

Last Updated Date : 20/05/2019