On a Stein And Weiss Property of the Conjugate Function
Keyword(s):
(1.1) The conjugate function on locally compact abelian groups. Let G be a locally compact abelian group with character group Ĝ. Let μ denote a Haar measure on G such that μ(G) = 1 if G is compact. (Unless stated otherwise, all the measures referred to below are Haar measures on the underlying groups.) Suppose that Ĝ contains a measurable order P: P + P ⊆P; PU(-P)= Ĝ; and P⋂(—P) =﹛0﹜. For ƒ in ℒ2(G), the conjugate function of f (with respect to the order P) is the function whose Fourier transform satisfies the identity for almost all χ in Ĝ, where sgnP(χ)= 0, 1, or —1, according as χ =0, χ ∈ P\\﹛0﹜, or χ ∈ (—P)\﹛0﹜.
1974 ◽
Vol 10
(1)
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pp. 59-66
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1989 ◽
Vol 40
(3)
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pp. 429-439
1975 ◽
Vol 12
(2)
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pp. 301-309
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1971 ◽
Vol 70
(1)
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pp. 31-47
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Keyword(s):
2010 ◽
Vol 88
(3)
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pp. 339-352
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1973 ◽
Vol 9
(2)
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pp. 291-298
1966 ◽
Vol 62
(3)
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pp. 399-420
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1973 ◽
Vol 9
(1)
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pp. 73-82
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