Fourier Series in Orthogonal Polynomials

A discussion of the structure of linear semigroups, that is, subsemigroups of the multiplicative semigroup Mn(K) of n x n matrices over a field K (or, more generally, skew linear semigroups - if K is allowed to be a division ring) and its applications to certain problems on associative algebras, semigroups and linear representations. It is motivated by several developments in the area of linear semigroups and their applications. It summarizes the state of knowledge in this area, presenting the results in a unified form. The book's point of departure is a structure theorem, which allows the use of powerful techniques of linear groups. Certain aspects of a combinatorial nature, connections with the theory of linear representations and applications to various problems on associative algebras are also discussed This book presents a course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. 1. Preliminaries -- 2. Orthogonal polynomials and their properties -- 3. Convergence and summability of Fourier series in L[subscript [mu]][superscript 2] -- 4. Fourier orthogonal series in L[subscript [mu]][superscript r] (1 < r < [infinity]) and C -- 5. Fourier polynomial series in L[subscript [mu]][superscript 1] Analogs of Fatou Theorems -- 6. The representations of the trilinear kernels. Generalized Translation Operator in orthogonal polynomials