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2 Rlemann Lebesgue Lemma
3 Convolution of two functions
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a(oc Abel absolute convergence absolutely continuous assumption B(oc Banach space belonging to L1 bounded functions bounded linear transformation bounded variation Cauchy limit Cauchy sequence Chapter class L1 complete metric space Conclusion condition continuous function converges convolution defined denote dense derivative doc oo dS(y dx)p dy oo element exists a function f and g f(oc f(x+h finite interval fixed fn(x following THEOREM formula Fourier transform func function f(x function given function of class H(Ru HQ(t implies integral inverse inversion-formula isometric kernel L1-function Let f(x Let K(oc Lg-norm lntegrable loci metric space monotonely norm null set obtain oo oo Parseval's relation principal class prove radial functions real numbers Remarks result Riemann integrable satisfies similarly SR(x step-functions T(oc Tauberian theorems theorem 11 theorem 9 tions trans uniformly unitary transformation vanishes variable W(oc Watson transform y(oc zero