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arXiv · 2106.06290

Polynomials of least deviation from zero in Sobolev $p$-norm

Abel Díaz-González·Héctor Pijeira-Cabrera·Javier Quintero-Roba
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Abstract

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev $p$-norm ($1<p<\infty$) for the case $p=1$. Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev $p$-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that, the $n$-th polynomial of least deviation has at least $n-\mathbf{d}^*$ zeros on the convex hull of the support of the measure, where $\mathbf{d}^*$ denotes the number of terms in the discrete part.

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Abel Díaz-González, Héctor Pijeira-Cabrera, Javier Quintero-Roba. 2021-12-16. Polynomials of least deviation from zero in Sobolev $p$-norm. https://arxiv.org/abs/2106.06290

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