Articles liés à Positive Harmonic Functions

Positive Harmonic Functions - Couverture souple

Pinsky, Ross G.

 
9780521059831: Positive Harmonic Functions
Couverture souple
ISBN 10 : 0521059836 ISBN 13 : 9780521059831
Editeur : Cambridge University Press, 2008

Synopsis

In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

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

Présentation de l'éditeur

In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

Revue de presse

Review of the hardback: 'This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.' European Mathematical Society Newsletter

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2008
Langue
anglais
ISBN 10 
0521059836
ISBN 13 
9780521059831
Reliure
Broché
Nombre de pages
492
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France