Document Type
Article
Publication Date
4-2022
Keywords
Optimal approximants; orthogonal polynomials; weakly inner functions; zero sets
Abstract
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a more complicated relationship between optimal approximants and orthogonal polynomials in weighted spaces. Weakly inner functions, whose optimal approximants are all constant, provide extreme cases where nontrivial orthogonal polynomials cannot be recovered from the optimal approximants. Concrete examples are presented to illustrate the general theory and are used to disprove certain natural conjectures regarding zeros of optimal approximants in several variables.
Citation
Sargent, M., & Sola, A. A. (2022). Optimal Approximants and Orthogonal Polynomials in Several Variables. Canadian Journal of Mathematics, 74 (2), 428-456. https://doi.org/10.4153/S0008414X20000826
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
