Displaying similar documents to “Lacunary series on compact groups”

Central sidonicity for compact Lie groups

Kathryn E. Hare (1995)

Annales de l'institut Fourier

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It is known that the dual of a compact, connected, non-abelian group may contain no infinite central Sidon sets, but always does contain infinite central p -Sidon sets for p > 1 . We prove, by an essentially constructive method, that the latter assertion is also true for every infinite subset of the dual. In addition, we investigate the relationship between weighted central Sidonicity for a compact Lie group and Sidonicity for its torus.

Spectral subspaces for the Fourier algebra

K. Parthasarathy, R. Prakash (2007)

Colloquium Mathematicae

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In this note we define and explore, à la Godement, spectral subspaces of Banach space representations of the Fourier-Eymard algebra of a (nonabelian) locally compact group.

The size of characters of compact Lie groups

Kathryn Hare (1998)

Studia Mathematica

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Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then μ n ∈ L 1 . When μ is a continuous, orbital measure then μ n is seen to belong to L 2 . Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).

Spectral decompositions and harmonic analysis on UMD spaces

Earl Berkson, T. Gillespie (1994)

Studia Mathematica

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We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for L X p to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X. ...

Spectral radius formula for commuting Hilbert space operators

Vladimír Muller, Andrzej Sołtysiak (1992)

Studia Mathematica

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A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].