Fourier Series In Orthogonal Polynomials

A presentation of a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. The first deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter Two contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters Three and Four are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L2m; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters Four and Five). 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 Four and Five is the representations of bilinear and trilinear forms obtained by the author. Chapters Two and Three (and part of Chapter One) should be useful to postgraduate students, and one can choose them for treatment.