An application of Banach algebra techniques for multiplicative functions.

Lutz Lucht

Displaying similar documents to “An application of Banach algebra techniques for multiplicative functions.”

A Mean-Value Theorem for Multiplicative Functions.

Karl-Heinz Indlekofer (1980)

Mathematische Zeitschrift

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Banach algebra techniques in the theory of arithmetic functions

Lutz G. Lucht (2008)

Acta Mathematica Universitatis Ostraviensis

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For infinite discrete additive semigroups $X \subset [0, \infty)$ we study normed algebras of arithmetic functions $g : X \to ℂ$ endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for $X = log ℕ$ . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras. ...