##### Department of Mathematics,

University of California San Diego

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### Functional Analysis

## Laurent Baratchart

#### INRIA

## Bounded extremal problems on the circle and Toeplitz operators

##### Abstract:

We consider the problem of best approximating a given function in $L^2$ of a subset of the unit circle by the trace of an $H^2$ function whose norm on the complementary set is bounded by a prescribed constant. It is known that the solution can be obtained by solving a spectral equation for a certain Toeplitz operator. We show how diagonalization of such an operator ‡ la Rosenblum-Rovnyak allows to estimate the rate of convergence. We also consider the same problem in $L^\infty$ rather than $L^2$ norm, and present its solution that involves some unbounded Toeplitz operator.

Host: Bill Helton

### November 12, 2004

### 10:00 AM

### AP&M 6218

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