Fourier algebras on tensor hypergroups

Amini, Massoud; Medghalchi, Alireza

doi:10.1090/conm/363/06637

Cited by 7 publications

(9 citation statements)

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“…We denote the linear span of A by lin(A). In the following theorem, in the case where K is a tensor hypergroup, we prove that our definition of A(K) coincides with that of Amini and Medghalchi (see [1]). Theorem 3.2 Let K be a locally compact 2-tensor hypergroup.…”

Section: Lemma 31 Let K Be a Locally Compact Hypergroup If C Is A Cmentioning

confidence: 61%

“…Recall the following definition from Section 1 of [1]. Definition 2.11 Let Σ be the set of all equivalent classes of continuous representations of the locally hypergroup K and S ⊆ Σ. Let…”

Section: Theorem 29 Let K Be a Locally Compact Hypergroup And Letmentioning

confidence: 99%

“…Amini and Medghalchi ( [1]) defined the Fourier-Stieltjs space B(K) for a locally compact hypergroup K as the linear span of P (K) (the set of bounded continuous positive-definite functions on K). Also they defined A(K) as the .…”

Section: Introductionmentioning

confidence: 99%

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Fourier algebras on locally compact hypergroups

Bami¹,

Pourgholamhossein

Samea

2008

Mathematische Nachrichten

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In the present paper we introduce a new definition for the Fourier space A (K) of a locally compact Hausdorff hypergroup K and prove that it is a Banach subspace of B (K). This definition coincides with that of Amini and Medghalchi in the case where K is a tensor hypergroup, and also with that of Vrem which is given only for compact hypergroups. We prove that Ap (K)* = PMq (K), where q is the exponent conjugate to p, in particular A (K)* = VN (K). Also we show that for Pontryagin hypergroups, A (K) = L2(K) * L2(K) = F (L1($ \hat K $)), where F stands for the Fourier transform on $ \hat K $. Furthermore there is an equivalent norm on A (K) which makes A (K) into a Banach algebra isomorphic with L1($ \hat K $). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Section: Lemma 31 Let K Be a Locally Compact Hypergroup If C Is A Cmentioning

confidence: 61%

Section: Theorem 29 Let K Be a Locally Compact Hypergroup And Letmentioning

confidence: 99%

See 1 more Smart Citation

Fourier algebras on locally compact hypergroups

Bami¹,

Pourgholamhossein

Samea

2008

Mathematische Nachrichten

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show abstract

“…For each

μ \in M (K)

, define

\hat{μ} \in {scriptE}_{\infty} (\overset{K}{true})

\hat{μ} (π) = \bar{π} (μ)

, then

μ \mapsto \hat{μ}

is a norm‐decreasing *‐isomorphism of

M (K)

into

{scriptE}_{\infty} (\overset{K}{true})

. Similarly one can define a norm‐decreasing *‐isomorphism

f \mapsto \hat{f}

L^{1} (K)

onto a dense subalgebra of

{scriptE}_{0} (\overset{K}{true})

[, 3.2, 3.3], . Also there is an isometric isomorphism

g \mapsto \hat{g}

L^{2} (K)

onto

{scriptE}_{2} (\overset{K}{true})

.…”

Section: Compact Hypergroupsmentioning

confidence: 99%

“…Similarly one can define a norm-decreasing * -isomorphism f →f of L 1 (K ) onto a dense subalgebra of E 0 K [12, 3.2, 3.3], [1]. Also there is an isometric isomorphism g →ĝ of L 2 (K ) onto E 2 K .…”

Section: Compact Hypergroupsmentioning

confidence: 99%