The Littlewood-Paley Theorem for Certain Disconnected Groups
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The first theorem of the type we are about to discuss was discovered by Paley . It is a theorem about Walsh series or, equivalently, about Fourier series on the Cantor group D2. In Appendix C we give a brief discussion of the relationship between Fourier analysis on the Cantor group and the theory of Walsh series on [0, 1]. Here now are a description and a proof of Paley’s theorem in the setting of harmonic analysis on D2.
KeywordsHaar Measure Dual Group Compact Abelian Group Open Subgroup Neighbourhood Base
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