Abstract view
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A Pointwise Estimate for the Fourier Transform and Maxima of a Function
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Published:2011-04-06
Printed: Dec 2012
Ryan Berndt,
Yale University and Otterbein College, Otterbein College, Westerville, Ohio 43081
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.
| Keywords: |
Fourier transform, maxima, two weight problem, roots, norm estimates, Dirichlet-Jordan theorem
Fourier transform, maxima, two weight problem, roots, norm estimates, Dirichlet-Jordan theorem
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