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A Pointwise Estimate for the Fourier Transform and Maxima of a Function

Published online by Cambridge University Press:  20 November 2018

Ryan Berndt
Ryan Berndt*
Affiliation:
Yale University and Otterbein College, Otterbein College, Westerville, Ohio 43081e-mail: rberndt@otterbein.edu
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Abstract

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We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the derivative of a function.

Keywords

42A3865T99Fourier transform, maximatwo weight problemrootsnorm estimatesDirichlet–Jordan theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 689 - 696
Copyright
Copyright © Canadian Mathematical Society 2012

References

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