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

2014/03/18 by Isaac Z. Pesenson, Pesenson, Isaac Z.
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1403.4564

Published in Math. Nachr. 282, No. 2, 253 - 269 (2009) / DOI 10.1002/mana.200510736

arxiv created 2014/03/18 · openalex publication_date 2014/03/18 · arxiv updated 2014/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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