Harmonic synthesis for subgroups

Carl S. Herz

Displaying similar documents to “Harmonic synthesis for subgroups”

A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert (1980)

Annales de l'institut Fourier

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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.

On the algebras $L_{p}$ of locally compact groups

Wiesław Żelazko (1961)

Colloquium Mathematicae

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On a class of convolution algebras of functions

Hans G. Feichtinger (1977)

Annales de l'institut Fourier

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The Banach spaces $Λ (A, B, X, G)$ defined in this paper consist essentially of those elements of $L^{1} (G)$ ( $G$ being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases $Λ (A, B, X, G)$ becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply...

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

Zhiguo Hu (1998)

Studia Mathematica

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Let A be a semisimple commutative regular tauberian Banach algebra with spectrum $Σ_{A}$ . In this paper, we study the norm spectra of elements of $\bar{s p a n} Σ_{A}$ and present some applications. In particular, we characterize the discreteness of $Σ_{A}$ in terms of norm spectra. The algebra A is said to have property (S) if, for all $φ \in \bar{} Σ_{A} 0$ , φ has a nonempty norm spectrum. For a locally compact group G, let $ℳ_{2}^{d} (Ĝ)$ denote the C*-algebra generated by left translation operators on $L^{2} (G)$ and $G_{d}$ denote the discrete group G. We prove...

The class of convolution operators on the Marcinkiewicz spaces

Ka-Sing Lau (1981)

Annales de l'institut Fourier

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Let $𝒯_{X}$ denote the operator-norm closure of the class of convolution operators $Φ_{μ} : X \to X$ where $X$ is a suitable function space on $R$ . Let $ℳ_{r}^{p}$ be the closed subspace of regular functions in the Marinkiewicz space $ℳ^{p}$ , $1 \leq p < \infty$ . We show that the space $𝒯_{ℳ_{r}^{p}}$ is isometrically isomorphic to $𝒯_{L^{p}}$ and that strong operator sequential convergence and norm convergence in $𝒯_{ℳ_{r}^{p}}$ coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener...

A note on $L_{p}$ -algebras

Wiesław Żelazko (1963)

Colloquium Mathematicae

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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.

Displaying similar documents to “Harmonic synthesis for subgroups”

A characterization of the minimal strongly character invariant Segal algebra

On the algebras L p of locally compact groups

On a class of convolution algebras of functions

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

The class of convolution operators on the Marcinkiewicz spaces

A note on L p -algebras

The support of a function with thin spectrum

On the algebras $L_{p}$ of locally compact groups

A note on $L_{p}$ -algebras