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Dirichlet series induced by the Riemann zeta-function

Jun-ichi Tanaka (2008)

Studia Mathematica

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ω , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form ( a p , s ) = ∏ p ( 1 - a p p - s ) - 1 for a p in ω . Among other things, using the Haar measure on ω for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.

Distances hilbertiennes invariantes sur un espace homogène

Jacques Faraut, Khelifa Harzallah (1974)

Annales de l'institut Fourier

Nous déterminons pour certains espaces homogènes X = G / K les distances invariantes qui proviennent d’un plongement de X dans un espace de Hilbert. Le carré d’une telle distance est un noyau de type négatif invariant dont nous donnons une représentation, c’est la formule de Lévy-Kinchine. Nous en déduisons que si G possède la propriété (T) de Kajdan une telle distance est toujours bornée.

Distinctness of spaces of Lorentz-Zygmund multipliers

Kathryn E. Hare, Parasar Mohanty (2005)

Studia Mathematica

We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Ditkin sets in homogeneous spaces

Krishnan Parthasarathy, Nageswaran Shravan Kumar (2011)

Studia Mathematica

Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.

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