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Search: All articles in the CMB digital archive with keyword Fourier transform

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1. CMB 2011 (vol 56 pp. 326)

Erdoğan, M. Burak; Oberlin, Daniel M.
 Restricting Fourier Transforms of Measures to Curves in $\mathbb R^2$ We establish estimates for restrictions to certain curves in $\mathbb R^2$ of the Fourier transforms of some fractal measures. Keywords:Fourier transforms of fractal measures, Fourier restrictionCategories:42B10, 28A12

2. CMB 2011 (vol 54 pp. 544)

Strungaru, Nicolae
 Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction In this paper we characterize the positive definite measures with discrete Fourier transform. As an application we provide a characterization of pure point diffraction in locally compact Abelian groups. Keywords:pure point diffraction, positive definite measure, Fourier transform of measuresCategory:43A25

3. 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 theoremCategories:42A38, 65T99

4. CMB 2010 (vol 54 pp. 159)