On algebraic properties of some q-multiple orthogonal polynomials

After an introductory discussion, in which the main notions and background materials of discrete multiorthogonality are addressed, we focus our attention on some new results, namely Chapters 2, 3, and 4. These three chapters constitute the main core of the Thesis. Indeed, Chapter 2 is focused on the study of four new families of q-multiple orthogonal polynomials, namely q-multiple Charlier, q-multiple Meixner of the first and second kind, respectively, and q-multiple Kravchuk. The raising operators and Rodrigues-type formulas, which provide an explicit expression for these new families, are obtained. Chapter 3 contains a detailed study of some algebraic properties for the aforementioned q-families of multiple orthogonal polynomials. More specifically, the (r + 1) order recurrence relation as well as the (r + 1) order difference equations in the discrete variable on the real line are obtained. Here the letter r is used to denote the dimension of the vector measure µ [vector] . Finally, in Chapter 4 some limit relations between the attained q-families of multiple orthogonal polynomials (when the parameter q approaches 1) and discrete multiple orthogonal polynomials are established. Programa Oficial de Doctorado en Ingeniería Matemática Presidente: Francisco José Marcellán Español.- Secretario: Alejandro Zarzo Altarejos.- Vocal: Manuel Enrique Mañas Baena