Abstract
In this chapter, we characterize interpolating and sampling sequences for the Fock spaces F α p. The characterizations are based on a certain notion of uniform density on the complex plane. So we will first spend some time discussing this geometric notion of density which also has applications in other areas of analysis and physics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Beurling, The Collected Works of Arne Beurling, vol. 2, (Harmonic Analysis, Boston, 1989)
P. Duren, A. Schuster, Bergman Spaces, (American Mathematical Society, Providence, RI, 2004)
K. Seip, Interpolation and Sampling in Spaces of Analytic Functions, (American Mathematical Society, Providence, RI, 2004)
K. Seip, Beurling type density theorems in the unit disk. Invent. Math. 113, 21–39 (1993)
K. Seip, Density theorems for sampling and interpolation in the Bargmann–Fock space. Bull. Amer. Math. Soc. 26, 322–328 (1992)
K. Seip, R. Wallstén, Density theorems for sampling and interpolation in the Bargmann–Fock space II. J. Reine Angew. Math. 429, 107–113 (1992)
J.Y. Tung, Zero sets and interpolating sets in Fock spaces. Proc. Amer. Math. Soc. 134, 259–263 (2005)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Zhu, K. (2012). Interpolating and Sampling Sequences. In: Analysis on Fock Spaces. Graduate Texts in Mathematics, vol 263. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8801-0_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8801-0_4
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-8800-3
Online ISBN: 978-1-4419-8801-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)