| Title:
|
Banach algebra techniques in the theory of arithmetic functions (English) |
| Author:
|
Lucht, Lutz G. |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
16 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
45-56 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Banach algebras |
| Keyword:
|
arithmetic functions |
| Keyword:
|
weighted norms |
| Keyword:
|
inversion |
| Keyword:
|
general Dirichlet series |
| Keyword:
|
Euler products |
| MSC:
|
11N37 |
| MSC:
|
11N56 |
| MSC:
|
40E10 |
| MSC:
|
46B25 |
| MSC:
|
46J99 |
| idZBL:
|
Zbl 1209.11089 |
| idMR:
|
MR2498636 |
| . |
| Date available:
|
2009-12-29T09:24:11Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137500 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
