A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert

Displaying similar documents to “A characterization of the minimal strongly character invariant Segal algebra”

On functions whose translates are independent

Ralph E. Edwards (1951)

Annales de l'institut Fourier

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Ce travail est l’étude de divers cas particuliers d’un problème nouveau, semble-t-il, concernant les translatées de fonctions ou de distributions sur un groupe. Soit $E$ un espace vectoriel topologique de fonctions ou de distributions sur un groupe abélien $G$ localement compact ; $E$ est supposé invariant par les translations $a \to f_{a} (x) = f (x + a) (f \in E, a \in G)$ . Si $f \in E$ et si $A$ est un sous-ensemble non vide de $G$ , $I (f, A) = I (f, A, E)$ désigne le sous-espace vectoriel fermé de $E$ engendré par les translatées $f_{a}$ de $f$ avec $a \in A$ . On dira qu’une $f \in E$ a ses...

Translation invariant forms on $L^{p} (G) (1 < p < \infty)$

Jean Bourgain (1986)

Annales de l'institut Fourier

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It is shown that if $G$ is a connected metrizable compact Abelian group and $1 < p < \infty$ , any (possibly discontinuous) translation invariant linear form on $L^{p} (G)$ is a scalar multiple of the Haar measure. This result extends the theorem of G.H. Meisters and W.M. Schmidt (J. Funct. Anal. 13 (1972), 407-424) on $L^{2} (G)$ . Our method permits in fact to consider any superreflexive translation invariant Banach lattice on $G$ , which is the adopted point of view. We study the representation of an element $f$ of this invariant...

The support of a function with thin spectrum

Kathryn Hare (1994)

Colloquium Mathematicae

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We prove that if $E \subseteq Ĝ$ does not contain parallelepipeds of arbitrarily large dimension then for any open, non-empty $S \subseteq G$ there exists a constant c > 0 such that $∥ f 1_{S} ∥_{2} \geq c ∥ f ∥_{2}$ for all $f \in L^{2} (G)$ whose Fourier transform is supported on E. In particular, such functions cannot vanish on any open, non-empty subset of G. Examples of sets which do not contain parallelepipeds of arbitrarily large dimension include all Λ(p) sets.

Geometric Fourier analysis

Antonio Cordoba (1982)

Annales de l'institut Fourier

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In this paper we continue the study of the Fourier transform on $R^{n}$ , $n \geq 2$ , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of $log (N)$ , where $N$ is the number of equal angles considered in $R^{2}$ . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of $R^{n}$ , $n \geq 2$ ,...

Operator Segal algebras in Fourier algebras

Brian E. Forrest, Nico Spronk, Peter J. Wood (2007)

Studia Mathematica

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Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator ${u \mapsto u |}_{H} : S ¹ A (G) \to A (H)$ , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup,...

Existence of large ε-Kronecker and FZI₀(U) sets in discrete abelian groups

Colin C. Graham, Kathryn E. Hare (2012)

Colloquium Mathematicae

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Let G be a compact abelian group with dual group Γ and let ε > 0. A set E ⊂ Γ is a “weak ε-Kronecker set” if for every φ:E → there exists x in the dual of Γ such that |φ(γ)- γ(x)| ≤ ε for all γ ∈ E. When ε < √2, every bounded function on E is known to be the restriction of a Fourier-Stieltjes transform of a discrete measure. (Such sets are called I₀.) We show that for every infinite set E there exists a weak 1-Kronecker subset F, of the same cardinality as E, provided there are...

On Ditkin sets

T. Muraleedharan, K. Parthasarathy (1996)

Colloquium Mathematicae

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In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter’s terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3])...

Infinite dimensional linear groups with a large family of $G$ -invariant subspaces

L. A. Kurdachenko, A. V. Sadovnichenko, I. Ya. Subbotin (2010)

Commentationes Mathematicae Universitatis Carolinae

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Let $F$ be a field, $A$ be a vector space over $F$ , $GL (F, A)$ be the group of all automorphisms of the vector space $A$ . A subspace $B$ is called almost $G$ -invariant, if ${dim}_{F} (B / {Core}_{G} (B))$ is finite. In the current article, we begin the study of those subgroups $G$ of $GL (F, A)$ for which every subspace of $A$ is almost $G$ -invariant. More precisely, we consider the case when $G$ is a periodic group. We prove that in this case $A$ includes a $G$ -invariant subspace $B$ of finite codimension whose subspaces are $G$ -invariant.

Unconditionality, Fourier multipliers and Schur multipliers

Cédric Arhancet (2012)

Colloquium Mathematicae

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Let G be an infinite locally compact abelian group and X be a Banach space. We show that if every bounded Fourier multiplier T on L²(G) has the property that $T \otimes I d_{X}$ is bounded on L²(G,X) then X is isomorphic to a Hilbert space. Moreover, we prove that if 1 < p < ∞, p ≠ 2, then there exists a bounded Fourier multiplier on $L^{p} (G)$ which is not completely bounded. Finally, we examine unconditionality from the point of view of Schur multipliers. More precisely, we give several necessary and sufficient...