Distributions and Fourier TransformsDistributions and Fourier Transforms |
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a₁ Accordingly analytic continuation analytic function arbitrary ball bounded function capacitary potential Co-function coefficients coincides compact subset compact support contained continuous function continuous linear converges uniformly convex function convex set convolution corresponding countable defined derivative difference quotients differential du(x dw(y equation everywhere finite total mass formula Fourier transform function f(x function of positive half-plane hence homogeneous of degree hypothesis inequality infinite infinity interval Lebesgue measure lemma linear functional linear space locally integrable function metric space monotone neighborhood obtain origin orthogonal polynomial positive measure positive Radon measure positive type PROOF radius Radon measure real axis satisfies semicontinuous seminorms sequence sphere subharmonic suppose supremum T₁ temperate distribution testfunction topology type set U₁ uniformly bounded upper half-plane variable x₁ zero