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# Analysis (Leader: Prof. Dmitry Khavinson <dkhavins (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'dkhavins' + '&#64;' + 'usf.edu' + '">Prof. Dmitry Khavinson</a>');)

## Friday, December 6, 2013

Title
Speaker
Time
Place

On minimal Haar covering of $$d$$-dimensional spaces, Part II
Boris Shekhtman
4:00pm-5:00pm
CMC 130

## Friday, November 29, 2013

Thanksgiving holiday — no seminar this week.

## Friday, November 22, 2013

Title
Speaker
Time
Place

On minimal Haar covering of $$d$$-dimensional spaces
Boris Shekhtman
4:00pm-5:00pm
CMC 130

Abstract

An $$n$$-dimensional subspace $$H$$ of $$C(K)$$ is called Haar if every non-zero function in $$H$$ has at most $$(n-1)$$ zeroes. Space of polynomials of degree $$n$$ is the prime example of a Haar space.

It is well-known that Haar spaces of functions of several (more than 1) variables do not exist. To compensate for this “loss of Haar” we introduce a notion of “Haar covering” and discuss some questions associated with this notion. In addition to approximation theory these questions are relevant to algebraic geometry (in the complex case) and algebraic topology (in the real case).

## Friday, November 15, 2013

Title
Speaker
Time
Place

Radial interpolation in the unit disc and related questions
Arthur Danielyan
4:00pm-5:00pm
CMC 130

Abstract

The talk will present a new approach for the peak-interpolation theorem of E. Bishop. We also discuss further interpolation problems and present new results in particular on the radial interpolation in the unit disc which are related to the Rudin-Carleson theorem.

## Friday, November 8, 2013

Title

Speaker
Time
Place

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants, Part III
E. A. Rakhmanov
4:00pm-5:00pm
CMC 130

## Friday, November 1, 2013

Title
Speaker
Time
Place

Groups $$\mathrm{SL}(2,R)$$ and its symmetric spaces
Igor Chitikov
4:00pm-5:00pm
CMC 130

Abstract

TBA

## Friday, October 25, 2013

Title

Speaker
Time
Place

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants, Part II
E. A. Rakhmanov
4:00pm-5:00pm
CMC 130

## Friday, October 18, 2013

Title
Speaker
Time
Place

Two dimensional orthogonal polynomials $$=$$ orthogonal polynomials on complex contours
Seung-Yeop Lee
4:00pm-5:00pm
CMC 130

Abstract

Motivated by the normal matrix ensemble with the external potential given by $$Q(z)=|z|^2+(\text{harmonic})$$, we study the special case where the corresponding orthogonal polynomials are equivalent to the orthogonal polynomials that are orthogonal with respect to certain contour integrals.

## Friday, October 11, 2013

Title

Speaker
Time
Place

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants
E. A. Rakhmanov
4:00pm-5:00pm
CMC 130

Abstract

Generalizations did not go too far yet. I am going to discuss some very recent progress in spirit of classical orthogonal polynomials based on DE for first kind Hermite-Padé polynomials for a special class of analytic function.

## Friday, October 4, 2013

Title
Speaker
Time
Place

Sharpness of connectivity bounds for quadrature domains, Part III
Seung-Yeop Lee
4:00pm-5:00pm
CMC 130

## Friday, September 27, 2013

Title
Speaker
Time
Place

Sharpness of connectivity bounds for quadrature domains, Part II
Seung-Yeop Lee
4:00pm-5:00pm
CMC 130

## Friday, September 20, 2013

Title
Speaker
Time
Place

Sharpness of connectivity bounds for quadrature domains
Seung-Yeop Lee
4:00pm-5:00pm
CMC 130

Abstract

Given the degree of a rational function, the “possible” topology of the associated quadrature domain can be identified (http://arxiv.org/pdf/1307.0487.pdf). We further claim that there exists a quadrature domain for each possible topology. This is a joint work with Nikolai Makarov.