Hilbert Space Methods
Let us denote by X the real line ℝ or the unit circle 𝕋. Then X̂ will denote, respectively, ℝ or ℤ; L2(X) will mean the same as L2(X, m) where m is Lebesgue measure on ℝ or normalized Lebesgue measure on 𝕋. The symbol L2(X̂) denotes L2 (ℝ, m) or ℓ2(ℤ).
KeywordsPlancherel Theorem Essential Support Bounded Spectrum Lebesgue Measurable Subset Card Versus
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