TY - JOUR

T1 - On the asymptotic behavior of the second moment of the Fourier transform of a random measure

AU - Esquivel, Manuel L.

PY - 2004

Y1 - 2004

N2 - The behavior at infinity of the Fourier transform of the random measures that appear in the theory of multiplicative chaos of Mandelbrot, Peyrière, and Kahane is an area quite unexplored. For context and further reference, we first present an overview of this theory and then the result, which is the main objective of this work, generalizing a result previously announced by Kahane. We establish an estimate for the asymptotic behavior of the second moment of the Fourier transform of the limit random measure in the theory of multiplicative chaos. After looking at the behavior at infinity of the Fourier transform of some remarkable functions and measures, we prove a formula essentially due to Frostman, involving the Riesz kernels.

AB - The behavior at infinity of the Fourier transform of the random measures that appear in the theory of multiplicative chaos of Mandelbrot, Peyrière, and Kahane is an area quite unexplored. For context and further reference, we first present an overview of this theory and then the result, which is the main objective of this work, generalizing a result previously announced by Kahane. We establish an estimate for the asymptotic behavior of the second moment of the Fourier transform of the limit random measure in the theory of multiplicative chaos. After looking at the behavior at infinity of the Fourier transform of some remarkable functions and measures, we prove a formula essentially due to Frostman, involving the Riesz kernels.

UR - http://www.scopus.com/inward/record.url?scp=17844395935&partnerID=8YFLogxK

U2 - 10.1155/S0161171204210183

DO - 10.1155/S0161171204210183

M3 - Article

SN - 0161-1712

VL - 2004

SP - 3423

EP - 3434

JO - International Journal Of Mathematics And Mathematical Sciences

JF - International Journal Of Mathematics And Mathematical Sciences

IS - 63

M1 - 671470

ER -