Ragnar Sigurðsson

collaborators

3 papers

math.CV2023

Polynomials with exponents in compact convex sets and associated weighted extremal functions -- The Bernstein-Walsh-Siciak theorem

Benedikt Steinar Magnússon, Ragnar Sigurðsson, Bergur Snorrason

We generalize the Bernstein-Walsh-Siciak theorem on polynomial approximation in $C^{n}$ to the case where the polynomial ring $P (C^{n})$ is replaced by a su…

math.CV2023

Polynomials with exponents in compact convex sets and associated weighted extremal functions -- The Siciak-Zakharyuta theorem

Benedikt Steinar Magnússon, Álfheiður Edda Sigurðardóttir, Ragnar Sigurðsson

The classical Siciak-Zakharyuta theorem states that the Siciak-Zakharyuta function $V_{E}$ of a subset $E$ of $C^{n}$ , also called a pluricomplex Green function or global exr…

math.CV2023

Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Fundamental results

Benedikt Steinar Magnússon, Álfheiður Edda Sigurðardóttir, Ragnar Sigurðsson +1

This paper is a survey of plurisubharmonic theory where the usual polynomial ring is replaced by a polynomial ring $P^{S} (C^{n})$ where the $m$ -th degree polynomials h…