Abstract
We show that a discrete sequence A of the complex plane is the union of n interpolating sequences for the Hörmander algebras A p if and only if the trace of A p on A coincides with the space of functions on A for which the divided differences of order n-1 are uniformly bounded. The analogous result holds in the unit disk for Korenblum-type algebras.
Mathematics Subject Classification (2000)
Keywords
Partially supported by the Picasso programme (Action Intégrée) HF2006-0211. First and second authors supported by MEC grant MTM2008-05561-C02-01 and CIRIT grant 2005-SGR 00611.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C.A. Berenstein and R. Gay, Complex Analysis and Special Topics in Harmonic Analysis, Springer Verlag, 1995.
C.A. Berenstein and B.Q. Li, Interpolating varieties for spaces of meromorphic functions, J. Geom. Anal. 5 (1995), 1–48.
J. Bruna and D. Pascuas, Interpolation in A -∞, J. London Math. Soc. (2) 40 (1989), no. 3, 452–466.
X. Massaneda Density conditions for interpolation in A -∞, J. Anal. Math. 79 (1999), 299–314.
X. Massaneda J. Ortega-Cerdà and M. Ounaïes, A geometric characterization of interpolation in \( \hat \varepsilon '(\mathbb{R})\) , Trans. Amer. Math. Soc. 358 (2006), 3459–3472.
M. Ounaïes, Interpolation by entire functions with growth conditions, Mich. Math. J. 56 (2008), no. 1, 155–171.
V.I. Vasyunin, Traces of bounded analytic functions on finite unions of Carleson sets Russian). Investigations on linear operators and the theory of functions, XII. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 126 (1983), 31–34.
V.I. Vasyunin, Characterization of finite unions of Carleson sets in terms of solvability of interpolation problems (Russian). Investigations on linear operators and the theory of functions, XIII. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 135 (1984), 31–35.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Massaneda, X., Ortega-Cerdà, J., Ounal’es, M. (2009). Traces of Hörmander Algebras on Discrete Sequences. In: Gustafsson, B., Vasil’ev, A. (eds) Analysis and Mathematical Physics. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9906-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-7643-9906-1_19
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9905-4
Online ISBN: 978-3-7643-9906-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)