Banach algebra techniques in the theory of arithmetic functions

Lutz G. Lucht

Acta Mathematica Universitatis Ostraviensis (2008)

  • Volume: 16, Issue: 1, page 45-56
  • ISSN: 1804-1388

Abstract

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For infinite discrete additive semigroups X ⊂ [ 0 , ∞ ) we study normed algebras of arithmetic functions g : X → 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.

How to cite

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Lucht, Lutz G.. "Banach algebra techniques in the theory of arithmetic functions." Acta Mathematica Universitatis Ostraviensis 16.1 (2008): 45-56. <http://eudml.org/doc/35175>.

@article{Lucht2008,
abstract = {For infinite discrete additive semigroups $X\subset [0,\infty )$ we study normed algebras of arithmetic functions $g\colon X\rightarrow \mathbb \{C\}$ endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for $X=\log \{\mathbb \{N\}\}$. 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.},
author = {Lucht, Lutz G.},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Banach algebras; arithmetic functions; weighted norms; inversion; general Dirichlet series; Euler products; arithmetic functions; weighted norms; Banach algebras},
language = {eng},
number = {1},
pages = {45-56},
publisher = {University of Ostrava},
title = {Banach algebra techniques in the theory of arithmetic functions},
url = {http://eudml.org/doc/35175},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Lucht, Lutz G.
TI - Banach algebra techniques in the theory of arithmetic functions
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2008
PB - University of Ostrava
VL - 16
IS - 1
SP - 45
EP - 56
AB - For infinite discrete additive semigroups $X\subset [0,\infty )$ we study normed algebras of arithmetic functions $g\colon X\rightarrow \mathbb {C}$ endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for $X=\log {\mathbb {N}}$. 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.
LA - eng
KW - Banach algebras; arithmetic functions; weighted norms; inversion; general Dirichlet series; Euler products; arithmetic functions; weighted norms; Banach algebras
UR - http://eudml.org/doc/35175
ER -

References

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