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An inequality for the distance between densities of free convolutions
densities of free convolutions inequality Probability
2011/8/24
Abstract: It is shown that under some conditions the distance between densities of free convolutions of two pairs of probability measures is smaller than the maximum of the Levy distance between the c...
We show that if p is an odd prime then p−1 X k=0 EkEp−1−k 1 (mod p) and p−3 X k=0 EkEp−3−k (−1)(p−1)/22Ep−3 (mod p),where E0,E1,E2, . . . are ...
A number of mathematical methods have been shown to model the zeroes of $L$-functions with remarkable success, including the Ratios Conjecture and Random Matrix Theory. In order to understand the str...
Multifractal structure of Bernoulli convolutions
Multifractal structure Bernoulli convolutions
2010/11/15
Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. T...
Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities
Infinite convolutions characteristic function entire functions
2010/12/1
We prove that certain quotients of entire functions are characteristic functions. Under some conditions,the probability measure corresponding to a characteristic function of that type has a density wh...
Convolutions of singular measures and applications to the Zakharov system
Convolution estimates transversal submanifolds L2 bounds
2010/12/8
Uniform L2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimen-sion. The results of Bennett-Bez are used to extend previous ...
Application of Holder inequality in generalised convolutions for functions with respect to k-symmetric points
Analytic functions k-symmetric points
2010/9/14
The two inequalities of the functions belonging to these two classes are the starlike and convex functions with respect to k-symmetric points, respectively. Some interesting properties of generalisati...
Reverse Weighted $L_p$ - Norm Inequalities in Convolutions
Convolution weighted $L_p$ inequality reverse Hö lder inequality inverse problems Green’s function integral transform stability
2008/6/27
Reverse Weighted $L_p$ - Norm Inequalities in Convolutions.