Holomorphic series expansion of functions of Carleman type

• Autorzy: Taib Belghiti
• Języki publikacji: EN

Abstrakty

EN

Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying $sup_{z∈Dₙ}|fₙ(z)| ≤ Cϱⁿ$ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f.

Kategorie tematyczne

• 30B10: Power series (including lacunary series)
• 30H05: Bounded analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 84
• Numer: 3
• Strony: 219-224

Daty

wydano

2004

Twórcy

autor

Taib Belghiti

• Department of Mathematics, Faculty of Sciences, B.P. 133, Kénitra, 14000, Morocco

Identyfikatory

DOI

10.4064/ap84-3-4