Interpolation of bounded sequences

Francesc Tugores

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 513-516
  • ISSN: 0011-4642

Abstract

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This paper deals with an interpolation problem in the open unit disc 𝔻 of the complex plane. We characterize the sequences in a Stolz angle of 𝔻 , verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on 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.

How to cite

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Tugores, Francesc. "Interpolation of bounded sequences." Czechoslovak Mathematical Journal 60.2 (2010): 513-516. <http://eudml.org/doc/38023>.

@article{Tugores2010,
abstract = {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.},
author = {Tugores, Francesc},
journal = {Czechoslovak Mathematical Journal},
keywords = {interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class; interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class},
language = {eng},
number = {2},
pages = {513-516},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interpolation of bounded sequences},
url = {http://eudml.org/doc/38023},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Tugores, Francesc
TI - Interpolation of bounded sequences
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 513
EP - 516
AB - 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.
LA - eng
KW - interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class; interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class
UR - http://eudml.org/doc/38023
ER -

References

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  1. Attele, K. R. M., 10.1017/S0017089500008521, Glasgow Math. J. 34 (1992), 35-41. (1992) Zbl0751.30032MR1145630DOI10.1017/S0017089500008521
  2. Carleson, L., 10.2307/2372840, Amer. J. Math. 80 (1958), 921-930. (1958) Zbl0085.06504MR0117349DOI10.2307/2372840
  3. Kotochigov, A. M., 10.1007/s10958-005-0339-0, J. Math. Sci. (N.Y.) 129 (2005), 4022-4039. (2005) Zbl1151.30339MR2037538DOI10.1007/s10958-005-0339-0
  4. Kronstadt, E. P., 10.2140/pjm.1976.63.169, Pacific J. Math. 63 (1976), 169-177. (1976) Zbl0306.30030MR0412431DOI10.2140/pjm.1976.63.169

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