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Regularization localization and support of distributions
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Analogously analytic function analytic representation antiderivative boundary values bounded C°°)-functions Cauchy kernel Cauchy representation Chapter characteristic function compact set compact support complex valued complex variables continuous function converges to zero converges uniformly convolution Corollary defined Definition denote dispersion relation distribution in 3D distribution with compact domain example Fubini's theorem func function f functions in 3D harmonic function Heaviside function Hence lim identity immediate consequence implies inverse Fourier transform L2-functions Let f Let f(t Let T G light cone locally integrable multiplier n-harmonic Note obtain open set Parseval's formula partition of unity polynomial Problem Proof proves the lemma proves the theorem quadrupole real axis Representation of distributions Section sense of 3D sequence tempered distribution tempered function tends to zero test functions tion topological space topology uniformly continuous upper half-plane vanishes z-plane