Van der Corput Lemma (Harmonic Analysis)
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High Quality Content by WIKIPEDIA articles! In mathematics, in the field of harmonic analysis, the van der Corput lemma is an estimate for oscillatory integrals named after the Dutch mathematician J. G. van der Corput. The following result is stated by E. Stein. The van der Corput lemma is closely related to the sublevel set estimates (see for example), which give the upper bound on the measure of the set where a function takes values not larger than epsilon,. Suppose that a real-valued function phi(x), is smooth on a finite or infinite interval IsubsetR, and that phi^{(k)}(x) ge 1, for all…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, in the field of harmonic analysis, the van der Corput lemma is an estimate for oscillatory integrals named after the Dutch mathematician J. G. van der Corput. The following result is stated by E. Stein. The van der Corput lemma is closely related to the sublevel set estimates (see for example), which give the upper bound on the measure of the set where a function takes values not larger than epsilon,. Suppose that a real-valued function phi(x), is smooth on a finite or infinite interval IsubsetR, and that phi^{(k)}(x) ge 1, for all xin I. There is a constant c_k,, which does not depend on phi,, such that for any epsilonge 0, the measure of the sublevel set {xin I: phi(x) leepsilon} is bounded by c_kepsilon^{1/k},.