Lp-Theory of Harish-Chandra Transform. Fourier Analysis on the Spaces ℓP(G//K)
The aim of the present chapter is to study the Lp-counter part of the L2-theory that was developed in Chapters 5 and 6. This will be done by studying the Harish-Chandra transforms of functions in a certain family of spaces ℓ P (G//K), 0 < p < 2. For p = 2, ℓ 2 is merely the space ℓ(G//K), while for p = 1, we get the L1-analogue of ℓ(G//K). The end result will be a complete characterization of the algebra of transforms of the spaces.
KeywordsFourier Analysis Asymptotic Expansion Wave Packet Simple Root Schwartz Space
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