Ana Loureiro University of Kent

An invitation for multiple orthogonality

Abstract:

I will invite you for a journey into the world of multiple orthogonal polynomials. These consist of a sequence of polynomials in a single variable and on a multi-index whose orthogonality is spread across a vector of measures. The main focus will be on those whose multi-index lies on the step line. They satisfy a number of properties that somehow mimic some observed in standard orthogonality. For instance, they satisfy linear recurrence relations of order higher than two. Throughout the talk I will go through several examples of such sequences and their overarching properties. Of course, the motivation and applications of them will also be part of the discussion.