Transforms of certain measures.

Cauchy Transforms of Self-Similar Measures

is a useful tool for numerical studies of the measure, since the measure of any reasonable set may be obtained as the line integral of F around the boundary. We give an effective algorithm for computing F when is a self-similar measure, based on a Laurent expansion of F for large z and a transformation law (Theorem 2.2) for F that encodes the self-similarity of . Using this algorithm we compute...

Laplace transforms of probability measures are there ?

A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.

Hypergeometric transforms in certain classes of analytic functions

Fourier Transforms of Lipschitz Functions on Certain Lie Groups

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the special linear group of real matrices of order two. 2000 Mathematics Subject Classification. 42A38, 44A15, 42C99, 44A05.

IF Approximation of Fourier Transforms and Certain Interpolating Splines

We extend to iP, X g p < °°, the L2 results of Bramble and Hilbert on convergence of discrete Fourier transforms and on approximation using smooth splines. The main tools are the estimates of [ 1 ] for linear functionals on Sobolev spaces and elementary results on Fourier multipliers.