Banach Algebra Methods in Prediction Theory.
The classical orthogonal polynomials defined on intervals of the real line are related to many important branches of analysis and applied mathematics. Here a method is described to generalise this concept to polynomials defined on higher dimensional spaces using Bi-Axial Monogenic functions. The particular examples considered are Gegenbauer polynomials defined on the interval [-1,1] and the Gegenbauer functions of the second kind which are weighted Cauchy integral transforms over this interval of...