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Mathematics > Complex Variables

arXiv:1006.2793 (math)
[Submitted on 7 Jun 2010 (v1), last revised 6 Apr 2011 (this version, v3)]

Title:On the range of composition operators on spaces of entire functions

Authors:S. Mukherjee, F. Jafari, J. E. McInroy
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Abstract:The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with affine maps. After some motivation demonstrating the importance of characterization of range spaces of bandlimited functions, in this paper we identify the subspaces of $ L^2 (\mathbb{R}) $ generated by these action. Extension of these theorems where Paley-Wiener spaces are replaced by the deBranges-Rovnyak spaces are given.
Comments: 11 Pages, Accepted for publication in Contemporary Mathematics, AMS
Subjects: Complex Variables (math.CV)
MSC classes: 32A15, 47B33, 47B32, 46E22
Cite as: arXiv:1006.2793 [math.CV]
  (or arXiv:1006.2793v3 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1006.2793
Journal reference: Contemporary Mathematics, Amer. Math. Soc. 547, 185-195, 2011

Submission history

From: Saikat Mukherjee [view email]
[v1] Mon, 7 Jun 2010 22:19:48 UTC (11 KB)
[v2] Tue, 26 Oct 2010 17:02:24 UTC (11 KB)
[v3] Wed, 6 Apr 2011 20:00:10 UTC (20 KB)
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