Abstract Harmonic Analysis

Hewitt, Edwin; Ross, Kenneth A.

doi:10.1007/978-1-4419-8638-2

Cited by 723 publications

(443 citation statements)

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“…The following example shows that B s (G) may not be a subalgebra of B(G) even when G is abelian (also see Hewitt and Ross [14], (19.21) and (19.26…”

Section: Decomposition Of B(g)mentioning

confidence: 96%

Decomposition of $B(G)$

Miao

1999

Trans. Amer. Math. Soc.

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“…The following example shows that B s (G) may not be a subalgebra of B(G) even when G is abelian (also see Hewitt and Ross [14], (19.21) and (19.26…”

Section: Decomposition Of B(g)mentioning

confidence: 96%

Decomposition of $B(G)$

Miao

1999

Trans. Amer. Math. Soc.

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“…The dual group of a compact group has the discrete topology [13]. Moreover if G is a compact abelian group then G is connected iff G is torsion-free [5]. This fact gives a clue to the results in this section.…”

Section: We Continue This To Obtainmentioning

confidence: 97%

On the vector-valued Fourier transform and compatibility of operators

Park

2005

Studia Math.

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Let G be a locally compact abelian group and let 1 < p ≤ 2. G ′ is the dual group of G, and p ′ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transformfor any G and positive integer n. And if the factor group of G with respect to its component of the identity element is a direct sum of a torsion free group and a finite group with discrete topology then F T G p = F T Z p .

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“…Everything is similar to Example 2.7, including the variants discussed in that example. The compactification is known as the set of q-adic integers (see [168], chapter 2).…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%