Geodesic
Banach algebra techniques in the theory of arithmetic functions
Communications in Mathematics, Tome 16 (2008) no. 1, pp. 45-56.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 11N37, 11N56, 40E10, 46B25, 46J99
Keywords: Banach algebras; arithmetic functions; weighted norms; inversion; general Dirichlet series; Euler products 
@article{COMIM_2008__16_1_a4,
     author = {Lucht, Lutz G.},
     title = {Banach algebra techniques in the theory of arithmetic functions},
     journal = {Communications in Mathematics},
     pages = {45--56},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2008},
     mrnumber = {2498636},
     zbl = {1209.11089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a4/}
}
TY  - JOUR
AU  - Lucht, Lutz G.
TI  - Banach algebra techniques in the theory of arithmetic functions
JO  - Communications in Mathematics
PY  - 2008
SP  - 45
EP  - 56
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a4/
LA  - en
ID  - COMIM_2008__16_1_a4
ER  - 
%0 Journal Article
%A Lucht, Lutz G.
%T Banach algebra techniques in the theory of arithmetic functions
%J Communications in Mathematics
%D 2008
%P 45-56
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a4/
%G en
%F COMIM_2008__16_1_a4
Lucht, Lutz G. Banach algebra techniques in the theory of arithmetic functions. Communications in Mathematics, Tome 16 (2008) no. 1, pp. 45-56. http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a4/