##### Department of Mathematics,

University of California San Diego

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### Advancement to Candidacy

## J.E. Pascoe

#### UCSD

## Boundary approximation and interpolation of multivariable Pick functions

##### Abstract:

Pick functions are the analytic maps of the upper half plane into itself. Their boundary behavior was studied classically by many household names such as Caratheodory, Julia and Nevanlinna. For example, Nevanlinna showed that asymptotic expansions of a certain type of Pick function at infinity parametrize the solutions to the Hamburger moment problem. We propose a program for studying interpolation and approximation multivariable Pick functions on the boundary using techniques from functional analysis which have roots in systems engineering.

### May 15, 2013

### 2:00 PM

### AP&M 5829

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