| Title:
|
Universally divergent Fourier series via Landau's extremal functions (English) |
| Author:
|
Herzog, Gerd |
| Author:
|
Kunstmann, Peer Chr. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
159-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence of functions $f\in A(\mathbb D)$, the Fourier series of which being universally divergent on countable subsets of $\mathbb T = \partial \mathbb D$. The proof is based on a uniform estimate of the Taylor polynomials of Landau's extremal functions on $\mathbb T\setminus\{1\}$. (English) |
| Keyword:
|
Fourier series |
| Keyword:
|
universal functions |
| Keyword:
|
Landau's extremal functions |
| MSC:
|
30B30 |
| MSC:
|
42A16 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 06433815 |
| idMR:
|
MR3338730 |
| DOI:
|
10.14712/1213-7243.2015.115 |
| . |
| Date available:
|
2015-04-25T16:59:20Z |
| Last updated:
|
2017-08-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144238 |
| . |
| Reference:
|
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| Reference:
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| . |
