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Bernstein–Nikolskii and Plancherel–Polya inequalities in Lp -norms on non-compact symmetric spaces

✍ Scribed by Isaac Pesenson


Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
211 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis


Abstract

By using Bernstein‐type inequality we define analogs of spaces of entire functions of exponential type in L~p~ (X), 1 ≤ p ≤ ∞, where X is a symmetric space of non‐compact. We give estimates of L~p~ ‐norms, 1 ≤ p ≤ ∞, of such functions (the Nikolskii‐type inequalities) and also prove the L~p~ ‐Plancherel–Polya inequalities which imply that our functions of exponential type are uniquely determined by their inner products with certain countable sets of measures with compact supports and can be reconstructed from such sets of “measurements” in a stable way (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)