AMS Chelsea Publishing 1958; 245 pp; hardcover Volume: 321 Reprint/Revision History: reprinted with corrections 1984; first AMS printing 2001 ISBN10: 0821828444 ISBN13: 9780821828441 List Price: US$36 Member Price: US$32.40 Order Code: CHEL/321.H
 From the Preface (1955): The first part of the present exposition is devoted to the theory of Toeplitz forms. The second part deals with applications, in particular to the calculus of probability and mathematical statistics. Neither part claims completeness in any way. Our purpose has been to elucidate the principal ideas of this remarkable chapter of modern analysis and to help the interested student of mathematical statistics to acquire a working knowledge of the subject. The somewhat protracted Chapter 1 explains not only the notation employed but contains also the definition of important auxiliary concepts and the exposition of basic results which will be used later. This arrangement avoids interruptions in the main text ... [It is assumed] that the reader is in possession of the fundamental facts of the theory of functions. "In chapters 2 and 3 certain topics appear which were treated in the book on orthogonal polynomials by G. Szegö. In view of the progress made in this subject since the publication of that book (1939) it was possible to bring some details in an improved setting. The other chapters contain partly old and partly more recent results, some older facts in a new setting, and finally some completely new results. Chapter 16 and Chapter 9 have been prepared by Szegö, the other chapters by Grenander ... " Readership Graduate students and research mathematicians. Table of Contents Part I: Toeplitz Forms  Preliminaries
 Orthogonal polynomials. Algebraic properties
 Orthogonal polynomials. Limit properties
 The trigonometric moment problem
 Eigenvalues of Toeplitz forms
 Generalizations and analogs of Toeplitz forms
 Further generalizations
 Certain matrices and integral equations of the Toeplitz type
Part II: Applications of Toeplitz Forms  Applications to analytic functions
 Applications to probability theory
 Applications to statistics
 Appendix: Notes and references
 Bibliography
 Index
