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ABC conjectureabstractabstract lang completenessactionadditive combinatoricsadele ringadic valuationaffine groupaffine spacesahiv22ahiv22supportalgebraic geometryalgorithmallow denyallows termalmost orthogonalityalmost periodicityanalysisanalytic number theoryanalytic setangular momentumangular velocityantichain operatorantichain tile countappendapprox hom pfrapproximationarcaritharithmetic geometryarithmetic progressionsas tensorasymptoticsasync runtimeauthorizationauthorizeauthorizerautomata theoryautomorphismauxiliaryball extensionball scalingbase changebase permbasicbasicsbasisbasis linearbatched evaluatorbehavioural theoryberlekamp welchbig opbijectivitybilinear formbindingbirthdaybisimulationbivariateblock rel distancebmobn254borel caratheodorybounding mutualbraketbridgebrownian motionbrun titchmarshbuchi congrbuchi congruencebuchi interbundledbundled semanticscaching logging oraclecaching oraclecadlagcadlag modificationcalculationscampanatocan reach 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Van der Corput

van_der_Corput

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Let $\varphi$ be $K$ -Lipschitz and bounded in norm by $B$ on $(a,b)$ . For every integer frequency $n$ ,

$\left\lVert\int_a^b e^{inx}\varphi(x)\,dx\right\rVert \le 2\pi(b-a)\left(B+\frac{K(b-a)}2\right)\left(1+|n|(b-a)\right)^{-1}.$

harmonic analysisFourier analysismeasure theory

Source project: Carleson formalization

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