6 papers
A Rudin-Carleson theorem with uniform approximation for manifold-valued maps
Benedikt Steinar Magnússon, Tyson Ritter
Given a closed set of measure zero and a continuous function , the classical Rudin-Carleson interpolation theorem states that…
A Rudin-Carleson theorem for multiply connected domains with interpolation
Benedikt Steinar Magnússon, Bergur Snorrason
Using an annular version of the F. and M. Riesz theorem, we prove a generalization of the Rudin-Carleson theorem for finitely connected bounded domains. That is, for a continuous f…
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 to the case where the polynomial ring is replaced by a su…
Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Characterization of polynomials by L2-estimates
Benedikt Steinar Magnússon, Álfheiður Edda Sigurðardóttir, Ragnar Sigurðsson +1
The main result of this paper is that an entire function that is in with respect to the weight is a polynomial with exponent…
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 of a subset of , also called a pluricomplex Green function or global exr…
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 where the -th degree polynomials h…