CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 42A38 ( Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type )

  Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2011 (vol 55 pp. 689)

Berndt, Ryan
A Pointwise Estimate for the Fourier Transform and Maxima of a Function
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:Fourier transform, maxima, two weight problem, roots, norm estimates, Dirichlet-Jordan theorem
Categories:42A38, 65T99

© Canadian Mathematical Society, 2014 : https://cms.math.ca/