Fourier transforms of unbounded measures

Surface Measures - Maximal Functions and Fourier Transforms

A Remark on Circular Means of Fourier Transforms of Measures

In [7] the optimal decay of circular L means of compactly supported measures of finite energy was given for p ≥ 2, with application to Falconer’s distance problem. The question was then raised in that paper as to whether any non-trivial improvement to these estimates were available for p < 2. We answer this question in the negative. This paper is concerned with the quantity σp(α) defined by Wol...

Oscillatory Integrals and Fourier Transforms of Surface Carried Measures

We suppose that S is a smooth hypersurface in Rn+1 with Gaussian curvature re and surface measure dS, it) is a compactly supported cut-off function, and we let pa be the surface measure with dßa = u>Ka dS. In this paper we consider the case where S is the graph of a suitably convex function, homogeneous of degree d, and estimate the Fourier transform ßa. We also show that if S is convex, with n...

Large Scale Renormalisation of Fourier Transforms of Self-similar Measures and Self-similarity of Riesz Measures

We shall show that the oscillations observed by Strichartz JRS92, Str90] in the Fourier transforms of self-similar measures have a large-scale renormali-sation given by a Riesz-measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.

Measurement of Plain Weave Fabrics Density Using Fourier Transforms

Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...