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Polynomial approximation of regular functions of a quaternionic variable

Szczepański Jerzy

Science, Technology and Innovation

2022

Vol. 16, no. 3-4

28--41

We consider Bernstein-Walsh-Siciak-type theorems on the polynomial approximation in the case of regular functions of one quaternionic variable and their applications to the uniform approximation and approximation in Lp norms with respect to measures satisfying the Bernstein-Markov condition.

Identity principles for Bernstein quasianalytic functions

Pleśniak W.

Commentationes Mathematicae

2013

Vol. 53, No. 2

79--88

We prove an identity principle for Bernstein quasianalytic functions on plane continua and study its extensions to the multivariate case.