We give an exposition of some simple but applicable cases of worst-case growth of a polynomial in terms of its uniform norm on a given compact set K ⊂ ℂd. Included is a direct verification of the formula for the pluripotential extremal function for a real simplex. Throughout we attempt to make the exposition as accessible to a general (analytic) audience as possible, avoiding wherever possible the finer details of Pluripotential Theory.
Extremal growth of polynomials
L. Bos;
2020-01-01
Abstract
We give an exposition of some simple but applicable cases of worst-case growth of a polynomial in terms of its uniform norm on a given compact set K ⊂ ℂd. Included is a direct verification of the formula for the pluripotential extremal function for a real simplex. Throughout we attempt to make the exposition as accessible to a general (analytic) audience as possible, avoiding wherever possible the finer details of Pluripotential Theory.
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