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Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness

A. Ülger (2014)

Colloquium Mathematicae

Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to...

Remotely c -almost periodic type functions in n

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely c -almost periodic functions in n , slowly oscillating functions in n , and further analyze the recently introduced class of quasi-asymptotically c -almost periodic functions...

Representations and Positive Definite Functions on Hypergroups

Nasr-Isfahani, A. (1999)

Serdica Mathematical Journal

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

Représentations de semi-groupes de mesures sur un groupe localement compact

Michel Duflo (1978)

Annales de l'institut Fourier

Soit T une distribution dissipative sur un groupe de Lie G et soit π une représentation fortement continue de G dans un espace de Banach. Supposons T à support compact. Il y a deux façons évidentes de définir un opérateur fermé π ( T ) : une faible et une forte. Le résultat principal de cet article est que l’on obtient le même résultat et que π ( T ) engendre un semi-groupe fortement continu d’opérateurs.

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