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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 example Fubini's theorem func function f(z function in 2D harmonic function Heaviside function Hence lim identity immediate consequence implies inverse Fourier transform L2-functions Let a(t Let f light cone linear functional locally integrable multiplier n-harmonic Note obtain open set Parseval's formula partition of unity Plancherel's theorem polynomial Problem Proof proves the lemma proves the theorem quadrupole real axis Representation of distributions Section sense of 2D sequence tempered distribution tempered function tends to zero test functions tion topology uniformly continuous upper half-plane vanishes z-plane