The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L²_m; summability almost everywhere by the Cesaro means and the Poisson–Abel method for Fourier polynomial series are the subject of Chapters 4 and 5).

The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials.

The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones.

Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment.

This book is intended for researchers (mathematicians, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.

Contents:

• Orthogonal Polynomials and Their Properties
• Convergence and Summability of Fourier Series in L²_m
• Fourier Orthogonal Series in L^r_m (1 < r < ¥) and C
• Fourier Polynomial Series in L¹_m. Analogs of Fatou Theorems
• The Representations of the Trilinear Kernels. Generalized Translation Operator in Orthogonal Polynomials

"... for experts in orthogonal polynomials, the most useful part of the book is the "Notes", where the author gives several precise additional comments on the results presented, on their origin and on their generalizations ... This book provides a comprehensive survey of this important subject."