USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

(Leader: Prof. Vilmos Totik )

Topic |
Wiener Lemma and Average Sampling |

Speaker 1 |
Qiyu Sun University of Central Florida |

Speaker 2 |
Vilmos Totik |

Topic |
Polynomial approximation with varying weights |

Time |
4:15-6:00 p.m. |

Place |
MAP 233 |

**Note:** This week, the seminar is joint with the Department of Mathematics at the University of Central Florida and will be held in Orlando.

**Title**

**Speaker**

**Time**

**Place**

Problems in the theory of boundary behavior of analytic functions and F. and M. Riesz Theorem

Arthur Danielyan

5:00pm-6:00pm

PHY 130

**Abstract**

Some problems and new results in boundary behavior of analytic functions will be discussed based on certain new association of a few well known classical results. A new simple proof of the boundary uniqueness theorem of F. and M. Riesz will be presented.

**Title**

**Speaker**

**Time**

**Place**

Interpolation Projections and Polynomial Ideals

Boris Shekhtman

5:00pm-6:00pm

PHY 130

**Abstract**

There is an interesting relation between interpolation projections, ideals of polynomials, resulting algebraic varieties and solutions of homogeneous DE with constant coefficients. These relationships are completely understood for polynomials of one variables. In my talk I will explore some known (and unknown) analogues for several variables. Hence the talk will contain a mixture of approximation theory, algebraic geometry and PDEs.

**Title**

**Speaker**

**Time**

**Place**

Zeros of orthogonal polynomials on the circle

Vilmos Totik

5:00pm-6:00pm

PHY 130

**Abstract**

It is shown (in joint work with Barry Simon), that there is a universal measure on the circle such that any probability measure on the unit disk is the limit of zero distribution of some subsequence of the corresponding orthogonal polynomials. This answers in a very strong sense a problem of Turán. The result is obtained by showing that one can freely prescribe the \(n\)-th orthogonal polynomial and \(N-n\) zeros of the \(N\)-th one. This is obtained by calculating the topological degree of a related mapping.