Oscillation of Fourier transform and Markov-Bernstein inequalities

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dc.creatorRevesz, Szilard Gy.
dc.creatorReyes, Noli N.
dc.creatorVelasco, Gino Angelo M.
dc.date2006-03-14
dc.date.accessioned2026-07-07T07:51:22Z
dc.date.available2026-07-07T07:51:22Z
dc.descriptionUnder certain conditions on an integrable function f having a real-valued Fourier transform Tf=F, we obtain a certain estimate for the oscillation of F in the interval [-C||f'||/||f||,C||f'||/||f||] with C>0 an absolute constant. Given q>0 and an integrable positive definite function f, satisfying some natural conditions, the above estimate allows us to construct a finite linear combination P of translates f(x+kq)(with k running the integers) such that ||P'||>c||P||/q, where c>0 is another absolute constant. In particular, our construction proves sharpness of an inequality of H. N. Mhaskar for Gaussian networks.
dc.identifierhttps://arxiv.org/abs/math/0603346
dc.identifierhttp://arxiv.org/abs/math/0603346
dc.identifierJournal of Approximation Theory 145 (2007), 100-110.
dc.identifierdoi:10.1016/j.jat.2006.07.004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125487
dc.subjectClassical Analysis and ODEs
dc.subject42A38, 41A17
dc.titleOscillation of Fourier transform and Markov-Bernstein inequalities
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