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Holomorphic series expansion of functions of Carleman type

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Belghiti T.

Annales Polonici Mathematici

2004

tom 84

nr 3

219-224

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.

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1 Annales Polonici Mathematici

1 Belghiti T.

1 2004

Wyniki wyszukiwania

Holomorphic series expansion of functions of Carleman type