The Fourier Integral and Certain of Its Applications

_ K₁ 1+t² ² dx absolutely convergent argument belongs to L₁ coefficients complete the proof const converges absolutely defined denumerable set e-iux dx einx 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 infinite 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 number of dimensions obtain periodic functions pertaining Plancherel theorem polynomial proof of theorem proposition prove real numbers Riesz-Fischer theorem Schwarz inequality sequence sin² step-function summable Tauberian theorem theorem 15 theory translation number uniformly values vanish zero αξ αξε Απε λα ΣΛ