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CONVOLUTIONS OF FUNCTIONS
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Abelian groups absolutely continuous appear Appendix apply approximate identity assertion assume Banach space bounded variation compact Abelian groups complex numbers complex-valued functions continuous functions continuous linear converges almost everywhere deduce defined denote diverge dual everywhere dense example Exercise exists finitely follows Fourier coefficients Fourier series Fourier transformation Frechet space g e L1 given group algebra harmonic analysis Hint homomorphism integrable functions invariant integral Kah2 Lebesgue lim sup linear functional linear subspace locally compact mapping Math metric neighborhood nonmeager nonnegative norm notation orthogonality relations Parseval formula partial sums periodic function pk(x points pointwise convergence pointwise representation positive definite functions positive numbers problem proof Prove reader real numbers real-valued Remarks satisfying Section seminorms sequence sNf(x subset sufficient Suppose theory topological group topological linear space trigonometric polynomials trigonometric series uniform boundedness principle verify zero