ISSN:
1432-0940
Keywords:
Interpolation
;
Equiconvergence
;
Distinguished set
;
Analytic functions
;
Radiusof convergence
;
41A05
;
41A25
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Letf∈A ρ (ρ〉1), whereA ρ denotes the class of functions analytic in ¦z¦ 〈ρ but not in ¦z¦≤ρ. For any positive integerl, the quantity Δ l,n−1(f; z) (see (2.3)) has been studied extensively. Recently, V. Totik has obtained some quantitative estimates for $$\overline {\lim _{n \to \infty } } \max _{\left| z \right| = R} \left| {\Delta _{l,n - 1}^ - \left( {f;z} \right)} \right|^{1/n} $$ . Here we investigate the order of pointwise convergence (or divergence) of Δ l,n−1(f; z), i.e., we study $$B_1 \left( {f;z} \right) = \overline {\lim _{n \to \infty } } \left| {\Delta _{l,n - 1} \left( {f;z} \right)} \right|^{1/n} $$ . We also study some problems arising from the results of Totik.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01890570
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