Homogeneous minimal polynomials with prescribed interpolation conditions
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- by Leokadia Białas-Cież and Jean-Paul Calvi PDF
- Trans. Amer. Math. Soc. 368 (2016), 8383-8402 Request permission
Abstract:
Given a compact set $E$ in $\mathbb {C}^{N+1}$, we consider the problem of finding a homogeneous polynomial of degree $d$ on $\mathbb {C}^{N+1}$ which deviates the least from zero on $E$ with respect to the uniform norm among all those satisfying interpolation conditions of the form $p(a)=f(a)$ where $a$ belongs to a given finite subset of $\mathbb {C}^{N+1}$ and $f$ is any function on such set. We show that this formalism enables one to recover several types of minimal polynomials previously studied and to prove a general invariance property of such minimal polynomials under polynomial mappings.References
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Additional Information
- Leokadia Białas-Cież
- Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, Institute of Mathematics, 30-059 Kraków, Poland
- Email: Leokadia.Bialas-Ciez@im.uj.edu.pl
- Jean-Paul Calvi
- Affiliation: Institut de Mathématiques, Université de Toulouse III and CNRS (UMR 5219), 31062, Toulouse Cedex 9, France
- Email: jean-paul.calvi@math.univ-toulouse.fr
- Received by editor(s): December 26, 2013
- Received by editor(s) in revised form: October 4, 2014
- Published electronically: January 6, 2016
- Additional Notes: The work of the first author was partially supported by the grant NCN Harmonia UMO-2013/08/M/ST1/00986.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 8383-8402
- MSC (2010): Primary 41A29, 41A05, 41A50, 41A63
- DOI: https://doi.org/10.1090/tran/6604
- MathSciNet review: 3551575