| Title:
|
Interpolation of bounded sequences (English) |
| Author:
|
Tugores, Francesc |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
513-516 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with an interpolation problem in the open unit disc $\mathbb D$ of the complex plane. We characterize the sequences in a Stolz angle of $\mathbb D $, verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on $\mathbb D $, but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions. (English) |
| Keyword:
|
interpolating sequence |
| Keyword:
|
Carleson's theorem |
| Keyword:
|
uniformly separated |
| Keyword:
|
Blaschke product |
| Keyword:
|
Lipschitz class |
| MSC:
|
30D50 |
| MSC:
|
30E05 |
| MSC:
|
41A05 |
| idZBL:
|
Zbl 1224.30175 |
| idMR:
|
MR2657965 |
| . |
| Date available:
|
2010-07-20T16:54:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140585 |
| . |
| Reference:
|
[1] Attele, K. R. M.: Interpolating sequences for the derivatives of Bloch functions.Glasgow Math. J. 34 (1992), 35-41. Zbl 0751.30032, MR 1145630, 10.1017/S0017089500008521 |
| Reference:
|
[2] Carleson, L.: An interpolation problem for bounded analytic functions.Amer. J. Math. 80 (1958), 921-930. Zbl 0085.06504, MR 0117349, 10.2307/2372840 |
| Reference:
|
[3] Kotochigov, A. M.: Free interpolation in the spaces of analytic functions with derivative of order s from the Hardy space.J. Math. Sci. (N.Y.) 129 (2005), 4022-4039. Zbl 1151.30339, MR 2037538, 10.1007/s10958-005-0339-0 |
| Reference:
|
[4] Kronstadt, E. P.: Interpolating sequences for functions satisfying a Lipschitz condition.Pacific J. Math. 63 (1976), 169-177. Zbl 0306.30030, MR 0412431, 10.2140/pjm.1976.63.169 |
| . |
