Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory - Couverture souple

Simon

 
9780821848630: Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory
Couverture souple
ISBN 10 : 0821848631 ISBN 13 : 9780821848630
Editeur : American Mathematical Society, 2005

Synopsis

This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szeg 's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2005
Langue
anglais
ISBN 10 
0821848631
ISBN 13 
9780821848630
Reliure
Broché
Nombre de pages
466
Coordonnées du fabricant
non disponible
Personne responsable
non disponible