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Paley-Wiener estimates for the Heisenberg group

✍ Scribed by Hartmut Führ

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
185 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The Paley‐Wiener space PW (G) on a stratified Lie group G is defined via the spectral decomposition of the associated sub‐Laplacian. In this paper, we show that functions in PW (ℍ), where ℍ denotes the Heisenberg group, extend to an entire function on the complexification ℍ~ℂ~, satisfying a growth estimate of exponential order two. We also show that a converse, characterizing elements of PW (ℍ) only in terms of pointwise growth behaviour of the entire extension, is not available (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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