The theory of orthogonal polynomials on the unit circle (OPUC) dates back to SzegÃ¶â€™s work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his survey paperâ€¦ (More)

On 25 February 1989, at a meeting of the British Society for the History of Mathematics, I heard the late Professor Philip Holgate deliver a lecture 'Independent functions. Probability and analysisâ€¦ (More)

Following the recent survey by the same author of SzegÃ¶â€™s theorem and orthogonal polynomials on the unit circle (OPUC) in the scalar case, we survey the corresponding multivariate prediction theoryâ€¦ (More)

In [BI3], we introduced the notion of ratio Mercerian theorem, to improve the Mercerian theorem for Fourier and Hankel transforms first proved in [BI1]. In the first half of this paper, we extendâ€¦ (More)

Motivated by the Category Embedding Theorem, as applied to convergent automorphisms [BOst11], we unify and extend the multivariate regular variation literature by a reformulation in the language ofâ€¦ (More)

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modernâ€¦ (More)

The recent popularity of copulas in the analysis and modelling of multivariate financial time series arises from several applications in the financial sector. This paper surveys the most importantâ€¦ (More)

We develop further the topological theory of regular variation of [BOst13]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group Tâ€¦ (More)

We define combinatorial principles which unify and extend the classical results of Steinhaus and Piccard on the existence of interior points in the distance set. Thus the measure and categoryâ€¦ (More)