Displaying similar documents to “On generalized power methods of limitation”

Perfect sets of finite class without the extension property

A. Goncharov (1997)

Studia Mathematica

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We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.

Arithmetical aspects of certain functional equations

Lutz G. Lucht (1997)

Acta Arithmetica

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The classical system of functional equations       1 / n ∑ ν = 0 n - 1 F ( ( x + ν ) / n ) = n - s F ( x ) (n ∈ ℕ) with s ∈ ℂ, investigated for instance by Artin (1931), Yoder (1975), Kubert (1979), and Milnor (1983), is extended to       1 / n ∑ ν = 0 n - 1 F ( ( x + ν ) / n ) = ∑ d = 1 ∞ λ n ( d ) F ( d x ) (n ∈ ℕ) with complex valued sequences λ n . This leads to new results on the periodic integrable and the aperiodic continuous solutions F:ℝ₊ → ℂ interrelating the theory of functional equations and the theory of arithmetic functions.