The Fourier Integral and Certain of Its Applications

absolutely convergent applied argument belongs to L₁ coefficients complete the proof const converges absolutely defined denumerable set e-iux dx eiux equivalent established everywhere exists finite interval finite number finite range fn(x follows Fourier integral Fourier series Fourier transform function f(x ƒ x Hence Index infinite K₁ K₁(x K₂ L₂ Lambert series Lebesgue integral lemma Let f(x let us notice let us put lim lim lim sup limited total variation M₁ measurable function Minkowski inequality modulus non-negative null set obtain Originally published periodic functions pertaining Plancherel theorem polynomial proof of theorem proposition prove real numbers revised edition Riesz-Fischer theorem sequence sin² step-function summable Tauberian theorem theorem 15 theory translation number uniformly values vanish Yellow Grundlehren zero αξ αξε Απε