## Rational Bases for Spaces of Holomorphic Functions in the Disc

**A 2011 Preprint by
G. Kyriazis and
P. Petrushev
**

- 2011:01
A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basic elements. The method is deployed to the construc- tion of bases consisting of rational functions of uniformly bounded degrees for Besov and Triebel-Lizorkin spaces of holomorphic functions in the unit disc. In turn, this is utilized to give a new proof of Pekarski's direct estimate for rational approximation of holomorphic functions in

*H*.^{p}