"Orthogonal Appell polynomials in arbitrary dimensions: the hypercomplex approach" by Isabel Cação, U. Aveiro (Portugal)

The definition of Appell polynomials of one real or complex variable was generalized to higher dimensions in the hypercomplex context by Malonek et al. in 2007 [1].  Later, in 2012, R. Láviscka [2] constructed complete orthogonal Appell systems of monogenic (or hyperholomorphic) polynomials by using the notion of Gelfand-Tsetlin bases. In this talk, we study some properties satisfied by those systems, such as three-term recurrence relations and second order differential equation in a similar way to the orthogonal polynomials of one real (or complex) variable. Moreover, we show that the process of construction of their building blocks relies only in the basic Appell sequence constructed by Malonek et al. [3]. 

References:
[1]  M. I. Falcão, H. R. Malonek, Generalized exponentials through Appell sets in R^{n+1} and Bessel functions, AIP Conference Proceedings, Vol. 936, 2007, pp. 738-741.
[2]  R. Láviscka, Complete Orthogonal Appell Systems for Spherical Monogenics, Complex Anal. Oper. Theory, 6 (2012) 477-489.
[3]  I. Cação, M. I. Falcão and H. R. Malonek, Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials, Adv. Appl. Clifford Álgebras, 15p., doi: 10.1007/s00006-015-0596-0.