Ellipses and Polynomial-to-Polynomial Mapping of Weighted Szego Projections

TL;DR

This paper investigates weighted Szego projections on ellipses and ellipsoids, demonstrating that on planar ellipses, these projections map polynomials to polynomials without degree increase, connecting potential theory with polynomial mappings.

Contribution

It establishes a polynomial-preserving property of weighted Szego projections on planar ellipses, linking potential theory and polynomial mappings in a novel way.

Findings

Weighted Szego projections map polynomials to polynomials on ellipses.

On planar ellipses, these projections do not increase polynomial degree.

The work connects potential theory with polynomial mapping properties.

Abstract

We take a look at weighted Szego projections on ellipses and ellipsoids in light of some known results of real and complex potential theory. We show that on planar ellipses there is a weighted Szego projection taking polynomials to polynomials without increasing degree.