## Dirichlet polynomials in connection with $\Phi$-widths and compressed sensing

- April 11, 2013
- 3:30 p.m.
- LeConte 412

## Abstract

Let $\Phi=\{\varphi _ i\}$ be a system of elements of Banach space $X$. We define $\Phi$-width of order $N$ of the set $A\subset X$ as a value of the optimal approximation (with respect to norm in $X$) of the set $A$ by the subspace generated by $N$ arbitrary elements of the system $\Phi$. This notion in the case when $\Phi$ is a trigonometric system was introduced in 1974 by R. Ismagilov. The talk is devoted to the $\Phi$-width estimates, their connections with "compressed sensing" and their application to the investigations of polynomials with respect to the system $\{n^{it}\}^\infty _ {n=1}$.