A Characterization of Minimal Homogeneous Banach Spaces

Feichtinger, Hans G.

doi:10.2307/2043985

Cited by 6 publications

(11 citation statements)

References 4 publications

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“…The second one, posed by the author himself, concerned the existence of smallest elements in certain families of Segal algebras (cf. [10] and [14]). As the reader will see below, the solution to both problems turnes out to be the same space So (G); this coincidence even considerably simplifies many arguments in proving further properties of So (G (G) and its dual S6 (G) have been given previously in two preliminary reports ( [12]) and in several lectures by the author, first in Vienna in February 1979.…”

Section: A Banach Space (B 11 H B) Which Is Continuously Embedded Inmentioning

confidence: 98%

On a new Segal algebra

Feichtinger

1981

Monatshefte f�r Mathematik

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Abstract. By means of a certain kind of 'atomic' representation a new Segal algebra So (G) of continuous functions on an arbitrary locally compact abelian group G is defined. From various characterizations ofS 0 (G), e. g. as smallest element within the family of all strongly character invariant Segal algebras, functorial properties of the symbol So are derived, which are similar to those of the space 5: (G) of Schwartz--Bruhat functions, e. g. invariance under the Fourier transform, or compatibility with restrictions to closed subgroups. The corresponding properties of its Banach dual $6 (G) as well as some of their applications are to be given in a subsequent paper.

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Section: A Banach Space (B 11 H B) Which Is Continuously Embedded Inmentioning

confidence: 98%

On a new Segal algebra

Feichtinger

1981

Monatshefte f�r Mathematik

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249

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“…The existence of V -well-spread sets for arbitrarily small V is proven in [4] (see also [16] for a generalization). Given a well-spread family X = (x i ) i∈I , a relatively compact neighborhood Q of e ∈ G and Y , we define the sequence space…”

Section: Introduction Coorbit Space Theory Was Originally Developed Bymentioning

confidence: 99%

Coorbit space theory for quasi-Banach spaces

Rauhut

2007

Studia Math.

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Abstract. We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces M p,q m , 0 < p, q ≤ ∞.

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“…This is a Segal algebra in L 1 (G), called the Lebesgue-Fourier algebra of G. We note that if G is unimodular, then LA(G) is a symmetric abstract Segal algebra in L 1 (G). Moreover, it is worthwhile to mention that the Weiner's algebra M 1 , see [13] and the Feichtinger's Segal algebra S 0 (G), see [4] and [19] are important examples of symmetric Segal algebras. As a consequence, we have the following.…”

Section: Then We Say That B Is a Symmetric Abstract Segal Algebra In Amentioning

confidence: 99%

A characterization of biflatness of Segal algebras based on a character

Essmaili

Rostami

Amini

2016

Glas. Mat. Ser. III

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Abstract. Let A be a Banach algebra and φ be a character on A. In this paper, we give a necessary condition, called condition (W ), for φ-biflatness of Banach algebra A as well as some hereditary properties. We also study the relation between left φ-amenability and condition (W ). Moreover, we apply these results and characterize the φ-biflatness of abstract symmetric Segal algebras. In particular, we identify φ-biflatness of the Lebesgue-Fourier algebra LA(G), where G is a unimodular locally compact group. These results describe a homological property for Segal algebras in the setting of biflatness based on character φ.

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A Characterization of Minimal Homogeneous Banach Spaces

Cited by 6 publications

References 4 publications

On a new Segal algebra

On a new Segal algebra

Coorbit space theory for quasi-Banach spaces

A characterization of biflatness of Segal algebras based on a character

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