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A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert (1980)

Annales de l'institut Fourier

For a locally compact, abelian group G , we study the space S 0 ( G ) of functions on G belonging locally to the Fourier algebra and with l 1 -behavior at infinity. We give an abstract characterization of the family of spaces { S 0 ( G ) : G abelian } by its hereditary properties.

Automatic continuity of operators commuting with translations

J. Alaminos, J. Extremera, A. R. Villena (2006)

Studia Mathematica

Let τ X and τ Y be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that Φ τ X ( t ) = τ Y ( t ) Φ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform

Detlev Poguntke (2010)

Colloquium Mathematicae

For any connected Lie group G and any Laplacian Λ = X²₁ + ⋯ + X²ₙ ∈ 𝔘𝔤 (X₁,...,Xₙ being a basis of 𝔤) one can define the commutant 𝔅 = 𝔅(Λ) of Λ in the convolution algebra ℒ¹(G) as well as the commutant ℭ(Λ) in the group C*-algebra C*(G). Both are involutive Banach algebras. We study these algebras in the case of a "distinguished Laplacian" on the "Iwasawa part AN" of a semisimple Lie group. One obtains a fairly good description of these algebras by objects derived from the semisimple group....

Central sidonicity for compact Lie groups

Kathryn E. Hare (1995)

Annales de l'institut Fourier

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.

Character sums in complex half-planes

Sergei V. Konyagin, Vsevolod F. Lev (2004)

Journal de Théorie des Nombres de Bordeaux

Let A be a finite subset of an abelian group G and let P be a closed half-plane of the complex plane, containing zero. We show that (unless A possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of A which belongs to P . In other words, there exists a non-trivial character χ G ^ such that a A χ ( a ) P .

Characterizations of amenable representations of compact groups

Michael Yin-Hei Cheng (2012)

Studia Mathematica

Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.

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