The Faber operator and its boundedness

[摘要] Let G be a domain bounded by a Jordan curve Gamma, and let A((G) over bar) be the Banach space of functions continuous on G and holomorphic in G. The Faber operator T is a linear mapping from A((D) over bar) to A((G) over bar) mapping w(n) onto the nth Faber polynomial F-n(=) (n = 0, 1, 2, ...). We show that parallel to Ti parallel to < infinity if Gamma is piecewise Dini-smooth, and give an example of a quasicircle Gamma for which parallel to T parallel to = infinity. (C) 1999 Academic Press.

[发布日期] 1999-12-01

[关键词] complex approximation;Faber operator