On a large class of non-linear coding methods based on Boolean invertible matrices

The main target of this work is to construct a large enumerated class of non- linear coding methods, based on a discrete invertible transform called Riesz Product, which is associated to a class of Boolean invertible matrices of order m ? m. The particular class of matrices is uniquely determined by a couple of permutations of the first m natural numbers {1, 2, ..., m}, so for any m = 1, 2, 3, ..., we get at least (m!)2 different non-linear coding methods. The resulting encoding/decoding method is very fast and requires low memory. It can be used both as a new encryption tool or as a Boolean random generator. .

Odometer action on Riesz product

We consider the Riesz product with a constant coefficient and odometer action over infinite product spaces. By studying the ratio set we can conclude the type of the above dynamical systems is III1.

Lp-convergence of a certain class of product martingales

We establish the Kakutani dichotomy property for two generalized Rademacher–Riesz product measures μ, ν that either μ, ν are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon–Nikodym derivative dμ/dν belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p ≧ 1.

The Maximal Spectral Type of a Rank One Transformation

In this paper it is shown that the maximal spectral type of a general rank one transformation is given by a kind of generalized Riesz product, with possibly some discrete measure.