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Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh, Yimin Xiao (2006)

Studia Mathematica

Let $X = X (t), t \in ℝ^{N}$ be a Gaussian random field in $ℝ^{d}$ with stationary increments. For any Borel set $E \subset ℝ^{N}$ , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.

We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.

Displaying 1 – 4 of 4

Images of Gaussian random fields: Salem sets and interior points

Interpolation by the Fourier-Stieltjes transform of a positive compactly supported measure

Interpolation harmonique sur les compacts

Interpolation sets for Fréchet measures

Currently displaying 1 – 4 of 4