Singular p-adic transformations for Bernoulli product measures

The Pascal adic transformation is loosely Bernoulli

The Pascal adic transformation is one of the simplest examples of adic transformations. We recall its construction by cutting and stacking and prove that it is loosely Bernoulli.  2003 Elsevier SAS. All rights reserved. Résumé La transformation Pascal adique est un des exemples les plus simples de transformations adiques. Nous rappelons sa construction par découpage et empilement et montrons q...

Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$

Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. So...

On a Multidimensional Volkenborn Integral and Higher Order Bernoulli Numbers

In particular, the values at x = 0 are called Bernoulli numbers of order k, that is, Bn (0) = Bn k) (see [1, 2, 4, 5, 9, 10, 14]). When k = 1, the polynomials or numbers are called ordinary. The polynomials Bn (x) and numbers Bn were first defined and studied by Norlund [9]. Also Carlitz [2] and others investigated their properties. Recently they have been studied by Adelberg [1], Howard [5], a...

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

p-Adic Measures and Bernoulli Numbers