Related papers: Donald Burkholder's work in martingales and analys…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the control of an appropriated maximal function. The case of…

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…

In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible…

This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a brief introduction to the theory of multiplicative integrals…

A review article on perturbation theory

A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.

We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.

The theory of fractal tilings of fractal blow-ups is extended to graph-directed iterated function systems, resulting in generalizations and extensions of some of the theory of Anderson and Putnam and of Bellisard et al. regarding…

We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.

Work in progress concerning alternative formalizations of arithmetic.

This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…

This paper contains my recollection of the creation and development of the so-called BFKL approach and my ideas about the ways of its further development.

This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. Furthermore, we gives a stochastic characterization for…

We give H\"older's inequalities for integral and conditional expectation involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for the operator are established.

This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.

Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. Rowlands

These short notes collect some thoughts about the way Butcher-Oemler-like and evolutionary studies are performed. We emphasize the shortcomings of several overlooked technical ingredients in the above type of studies, with the hope of…