EL-FALLAH, Omar; KELLAY, Karim; MASHREGHI, Javad; RANSFORD, Thomas

doi:10.1017/CBO9781107239425

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

EL-FALLAH, Omar
Département de Mathématiques

KELLAY, Karim
Institut de Mathématiques de Bordeaux [IMB]

MASHREGHI, Javad
Département de Mathématiques et de Statistiques

Idioma

Ouvrage

Este ítem está publicado en

2014-01-14p. 230

Cambridge University Press

Resumen en inglés

The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.< Leer menos

Metadatos

Compartir este ítem

Licencia de uso del documento

A primer on the Dirichlet Spaces

Idioma

Este ítem está publicado en

Resumen en inglés

URI

DOI

Orígen

Centros de investigación