Articles liés à LMS: 199 Invariant Potential Theory

LMS: 199 Invariant Potential Theory - Couverture souple

Livre 174 sur 387: London Mathematical Society Lecture Notes

Stoll, Manfred

 
9780521468305: LMS: 199 Invariant Potential Theory
Couverture souple
ISBN 10 : 0521468302 ISBN 13 : 9780521468305
Editeur : Cambridge University Press, 2008

Synopsis

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

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

Présentation de l'éditeur

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

Revue de presse

"The topics included in this book are well chosen and well presented." Walter Rudin, Bulletin of the American Mathematical Society

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 
0521468302
ISBN 13 
9780521468305
Reliure
Broché
Nombre de pages
184
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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