L1-norm estimates of character sums defined by a Sidon set in the dual of a compact Kac algebra

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Erscheinungsjahr:
2013
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Text
Schlagworte:
  • Character
  • Compact kac algebra
  • Fourier transform
  • Helgason-Sidon set.
  • Sidon set
  • Strong sidon set
Beschreibung:
  • We generalize the following fact to compact Kac algebras: Let G be a compact abelian group, and let f be any trigonometric polynomial on G, whose Fourier transform f̂ vanishes outside of a Sidon set E in the dual, discrete abelian group G{cyrillic} of G. Then we have {norm of matrix} f {norm of matrix}2 ≥ KE{norm of matrix} f {norm of matrix}1, where KE is a constant depending only on E. For this generalization, we introduce the notion of Helgason-Sidon sets, which is based on S. Helgason's work on lacunary Fourier series on arbitrary compact groups. We establish the above inequality for all finite linear combinations of characters defined by a Helgason-Sidon set in the set of all minimal central projections. © THETA, 2013.
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  • info:eu-repo/semantics/closedAccess
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oai:www.edit.fis.uni-hamburg.de:publications/2482169e-a7a5-487a-939a-75fb5eb64021