Open Access
may 2014 Carleman Type Approximation Theorem in the Quaternionic Setting and Applications
Sorin G. Gal, Irene Sabadini
Bull. Belg. Math. Soc. Simon Stevin 21(2): 231-240 (may 2014). DOI: 10.36045/bbms/1400592621


In this paper we prove Carleman's approximation type theorems in the framework of slice regular functions of a quaternionic variable. Specifically, we show that any continuous function defined on $\mathbb{R}$ and quaternion valued, can be approximated by an entire slice regular function, uniformly on $\mathbb{R}$, with an arbitrary continuous "error" function. As a byproduct, one immediately obtains result on uniform approximation by polynomials on compact subintervals of $\mathbb{R}$. We also prove an approximation result for both a quaternion valued function and its derivative and, finally, we show some applications.


Download Citation

Sorin G. Gal. Irene Sabadini. "Carleman Type Approximation Theorem in the Quaternionic Setting and Applications." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 231 - 240, may 2014.


Published: may 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1302.30065
MathSciNet: MR3211012
Digital Object Identifier: 10.36045/bbms/1400592621

Primary: 30G35‎
Secondary: 30E10

Keywords: Carleman approximation theorem , entire functions , slice regular functions

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 2 • may 2014
Back to Top