Communications in Mathematical Physics

, Volume 349, Issue 3, pp 895–945 | Cite as

Lacunary Fourier Series for Compact Quantum Groups

Article

Abstract

This paper is devoted to the study of Sidon sets, \({\Lambda(p)}\)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, \({\Lambda(p)}\)-sets and lacunarities for Lp-Fourier multipliers, generalizing a previous work by Blendek and Michalic̆ek. We also prove the existence of \({\Lambda(p)}\)-sets for orthogonal systems in noncommutative Lp-spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included.

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance
  2. 2.Institute of MathematicsPolish Academy of SciencesWarszawaPoland

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