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The Fourier Coefficients
Recapturing from c
6 other sections not shown
analagous analytic Banach algebra Banach space Cauchy compact subsets complex number compute consider continuous function continuous linear functional continuous periodic function converges uniformly Corollary deduce defined denote differential equation Dini condition Dirichlet kernel Dirichlet problem everywhere Example Exercise exists exponential fGL1 finite Fourier coefficients Fourier series Fourier transform Fubini's theorem function g G L1 G L2 Gelfand transform given harmonic heat equation hence Hilbert space Hint inner product integrable function interval inversion formula L1 function Laplace transform Laplace's equation Lebesgue set Lemma mapping multiplication nonnegative norm notation one-to-one orthonormal partial sums periodic function point of continuity pointwise Poisson integral Poisson kernel polynomials proof of Theorem properties Prove Theorem real numbers result satisfies Section 5.2 Show singular kernel solution structure space summable Suppose theory trigonometric uniform convergence uniformly bounded vanishes