| Title:
|
Blockwise interpolation on sequences of points in the disk (English) |
| Author:
|
Tugores, Laia |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
61 |
| Issue:
|
5 |
| Year:
|
2025 |
| Pages:
|
187-194 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note deals with the classical topic of interpolating bounded sequences of complex numbers by bounded analytic functions on sequences in the unit disk. We introduce linear, polynomial, and multiplicative interpolation over fixed-length consecutive blocks of points taken from these sequences, and examine the corresponding interpolating sequences. (English) |
| Keyword:
|
interpolating sequences |
| Keyword:
|
bounded analytic functions |
| Keyword:
|
separated sequences |
| MSC:
|
30E05 |
| MSC:
|
30H05 |
| MSC:
|
30J10 |
| idZBL:
|
Zbl 08162264 |
| DOI:
|
10.5817/AM2025-5-187 |
| . |
| Date available:
|
2026-01-23T11:41:01Z |
| Last updated:
|
2026-03-16 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153283 |
| . |
| Reference:
|
[1] Carleson, L.: An interpolation problem for bounded analytic functions.Amer. J. Math. 80 (1958), 921–930. Zbl 0085.06504, 10.2307/2372840 |
| Reference:
|
[2] Garnett, J.B.: Bounded analytic functions.Grad. Texts in Math., vol. 236, Springer Verlag, New York, 2006, revised 1st. MR 2261424 |
| Reference:
|
[3] Tugores, F.: Recursive interpolating sequences.Open Math. 16 (2018), 461–468. MR 3797927, 10.1515/math-2018-0044 |
| Reference:
|
[4] Tugores, F., Tugores, L.: Interpolation by differences in $H^\infty $.Stud. Sci. Math. Hungar. 58 (2021), 157–162. MR 4296469 |
| . |
