The Fourier Integral and Certain of Its Applications

_ ƒ ² dx absolutely convergent analytic APPLICATIONS HE FOURIER argument belongs to L2 bounded calculus chess coefficients complete the proof const defined denumerable set differential equations e-iux dx einx eiux equivalent established exists finite interval finite number finite range follows formulae FOURIER INTEGRAL Fourier series Fourier transform function f(x ƒ x geometry Hence infinite introduction K₁ K₁(x K₂ Konrad Knopp L₁ L₂ Lambert series Lebesgue integral lemma lim lim lim sup linear logic M₁ math mathematicians mathematics methods Minkowski inequality modulus non-negative normal set null set Paperbound periodic functions pertaining physics Plancherel theorem polynomial problems proof of theorem proposition puzzles Riemann Riesz-Fischer theorem sequence sin² step-function term theorem 15 THEORY OF FUNCTIONS translation number uniformly values vanish zero αξ αξε