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On averages of randomized class functions on the symmetric groups and their asymptotics

Paul-Olivier Dehaye, Dirk Zeindler (2013)

Annales de l’institut Fourier

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...

On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups

Leszek Skrzypczak (1998)

Commentationes Mathematicae Universitatis Carolinae

In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.

On Beurling measure algebras

Ross Stokke (2022)

Commentationes Mathematicae Universitatis Carolinae

We show how the measure theory of regular compacted-Borel measures defined on the δ -ring of compacted-Borel subsets of a weighted locally compact group ( G , ω ) provides a compatible framework for defining the corresponding Beurling measure algebra ℳ ( G , ω ) , thus filling a gap in the literature.

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

Let 𝔤 be a complex reductive Lie algebra and 𝔨 ⊂ 𝔤 be any reductive in 𝔤 subalgebra. We call a ( 𝔤 , 𝔨 ) -module M bounded if the 𝔨 -multiplicities of M are uniformly bounded. In this paper we initiate a general study of simple bounded ( 𝔤 , 𝔨 ) -modules. We prove a strong necessary condition for a subalgebra 𝔨 to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded ( 𝔤 , 𝔨 ) -module, and then establish a sufficient condition for a subalgebra 𝔨 to be bounded (Theorem 5.1). As a result we are able to...

On character amenable Banach algebras

Z. Hu, M. Sangani Monfared, T. Traynor (2009)

Studia Mathematica

We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...

On characterized subgroups of Abelian topological groups X and the group of all X -valued null sequences

S. S. Gabriyelyan (2014)

Commentationes Mathematicae Universitatis Carolinae

Let X be an Abelian topological group. A subgroup H of X is characterized if there is a sequence 𝐮 = { u n } in the dual group of X such that H = { x ∈ X : ( u n , x ) → 1 } . We reduce the study of characterized subgroups of X to the study of characterized subgroups of compact metrizable Abelian groups. Let c 0 ( X ) be the group of all X -valued null sequences and 𝔲 0 be the uniform topology on c 0 ( X ) . If X is compact we prove that c 0 ( X ) is a characterized subgroup of X ℕ if and only if X ≅ 𝕋 n × F , where n ≥ 0 and F is a finite Abelian group. For every compact Abelian...

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