Weighted energy problem on the unit circle
Igor E. Pritsker
TL;DR
This paper addresses the weighted energy problem on the unit circle by determining the extremal measure and its support, with applications to polynomial and exponential weights, advancing understanding in potential theory.
Contribution
It provides a solution to the weighted energy problem on the unit circle and characterizes the extremal measure and its support, including applications to specific weight functions.
Findings
Explicit extremal measure on the unit circle
Characterization of the support of the extremal measure
Applications to polynomial and exponential weights
Abstract
We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.
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Taxonomy
TopicsMathematical functions and polynomials · Analytic and geometric function theory · Holomorphic and Operator Theory