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arXiv · 2009.01793

Optimal approximants and orthogonal polynomials in several variables II: families of polynomials in the unit ball

Meredith Sargent·Alan A. Sola
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Abstract

We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$ and a scale of Hilbert function spaces in the unit $2$-ball having reproducing kernel $(1-\langle z,w\rangle)^{-γ}$, $γ>0$. Our arguments are elementary but do not rely on reduction to the one-dimensional case.

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Meredith Sargent, Alan A. Sola. 2020-09-03. Optimal approximants and orthogonal polynomials in several variables II: families of polynomials in the unit ball. https://arxiv.org/abs/2009.01793

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