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

Authors

Ryan Berndt, Otterbein UniversityFollow

Document Type

Article

Publication Date

12-2012

Publication Title

Canadian Mathematical Bulletin

Keywords

Pointwise Estimate, Fourier Transform, Theorem

Abstract

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.

First Page

689

Last Page

696

Volume

55

Issue

4

Repository Citation

Berndt, Ryan, "A Pointwise Estimate for the Fourier Transform and the Number of Maxima of a Function" (2012). Mathematics Faculty Scholarship. 10.
https://digitalcommons.otterbein.edu/math_fac/10

Original Citation

Berndt, R. "A Pointwise Estimate For The Fourier Transform And Maxima Of A Function." Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 55.4 (n.d.): 689-696.

Version

Pre-Print

Publisher's Statement

Copyright (c) 2012 Institute for Scientific Information