Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions.We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite- Padé approximation in matrix form is given

Historic buildings and the creation of experiencescapes: looking to the past for future success

Purpose: The purpose of this paper is to identify the role that the creative re-use of historic buildings can play in the future development of the experiences economy. The aesthetic attributes and the imbued historic connotation associated with the building help create unique and extraordinary “experiencescapes” within the contemporary tourism and hospitality industries. Design/methodology/approach: This paper provides a conceptual insight into the creative re-use of historic buildings in the tourism and hospitality sectors, the work draws on two examples of re-use in the UK. Findings: This work demonstrates how the creative re-use of historic buildings can help create experiences that are differentiated from the mainstream hospitality experiences. It also identifies that it adds an addition unquantifiable element that enables the shift to take place from servicescape to experiencescape. Originality/value: There has been an ongoing debate as to the significance of heritage in hospitality and tourism. However, this paper provides an insight into how the practical re-use of buildings can help companies both benefit from and contribute to the experiences economy

Orthogonal polynomial interpretation of q-Toda and q-Volterra equations

The correspondences between dynamics of q-Toda and q-Volterra equations for the coefficients of the Jacobi operator and its resolvent function are established. The orthogonal polynomials associated with these Jacobi operators satisfy an Appell condition, with respect to the q-difference operator Dq . Lax type theorems for the point spectrum of the Jacobi operators associated with these equations are obtained. Examples related with the big q-Legendre, discrete q-Hermite I, and little q-Laguerre orthogonal polynomials and q-Toda and q-Volterra equations are given

Riemann-Hilbert problems for multiple orthogonal polynomials

In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 2 matrix functions) associated which a system of orthogonal polynomials. This Riemann-Hilbert problem was later used by Deift et al. and Bleher and Its to obtain interesting results on orthogonal polynomials, in particular strong asymptotics which hold uniformly in the complex plane. In this paper we will show that a similar Riemann-Hilbert problem (for (r + 1) (r + 1) matrix functions) is associated with multiple orthogonal polynomials. We show how this helps in understanding the relation between two types of multiple orthogonal polynomials and the higher order recurrence relations for these polynomials. Finally we indicate how an extremal problem for vector potentials is important for the normalization of the Riemann-Hilbert problem. This extremal problem also describes the zero behavior of the multiple orthogonal polynomials. 1 Introduction Recently it was observed that ..

On the Scientific Work of Konstantin Ilyich Oskolkov

This chapter is a brief account of the life and the scientific work of K.I. Oskolkov