A First Course in Harmonic AnalysisThis primer in harmonic analysis gives a lean and stream-lined introduction to the central concepts of this beautiful theory. In contrast to other books on the topic, A First Course in Harmonic Analysis is entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Nevertheless, almost all proofs are given in full and all central concepts are presented clearly. This book introduces Fourier analysis, leading up to the Poisson Summation Formula, as well as the techniques used in harmonic analysis of noncommutative groups. |
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assume C+ G called Cauchy sequence Cc(G Chapter characters complete complex vector space compute continuous function continuously differentiable convergence theorem converges pointwise converges uniformly convolution countable d₁ define denote dense Examples finite abelian group follows Fourier coefficients Fourier series Fourier transform function f ƒ and g given gives GL(V group G group homomorphism Haar integral harmonic analysis hence Hilbert space Hint implies inner product interval invariant integral isometry isomorphic L2-norm l²(A l²(S LCA group Let f Let ƒ Let G Lie algebra Lie(G locally compact Matn metric space natural number neighborhood nonnegative norm open set orthonormal basis path connected periodic function Plancherel's theorem pre-Hilbert space Proof Proposition prove Q.E.D. Theorem Re(s real numbers Riemann integrable satisfies sequence vn Show subset subspace tends to zero Theory topology triangle inequality V₁ μο