Abstract
We consider the problem of characterizing the extreme points of the set of analytic functions on the bidisk with positive real part and . If one restricts to those whose Cayley transform is a rational inner function, one gets a more tractable problem. We construct families of such that are extreme points and conjecture that these are all such extreme points. These extreme points are constructed from polynomials dubbed -saturated, which roughly speaking means they have no zeros in the bidisk and as many zeros as possible on the boundary without having infinitely many zeros.
Citation
Greg Knese. "Extreme points and saturated polynomials." Illinois J. Math. 63 (1) 47 - 74, June 2019. https://doi.org/10.1215/00192082-7600059
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