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A primer on the Dirichlet space

El-Fallah, Omar.

A primer on the Dirichlet space

Record Type:	Electronic resources : Monograph/item
Title/Author:	A primer on the Dirichlet spaceOmar El-Fallah ... [et al.].
other author:	El-Fallah, Omar.
Published:	Cambridge :Cambridge University Press,2014.
Description:	xiii, 211 p. :ill., digital ;24 cm.
Subject:	Dirichlet principle.
Online resource:	https://doi.org/10.1017/CBO9781107239425
ISBN:	9781107239425$q(electronic bk.)

A primer on the Dirichlet space
A primer on the Dirichlet space[electronic resource] /Omar El-Fallah ... [et al.]. - Cambridge :Cambridge University Press,2014. - xiii, 211 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;203. - Cambridge tracts in mathematics ;96..

Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma.

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.

ISBN: 9781107239425$q(electronic bk.)Subjects--Topical Terms:

840381
Dirichlet principle.

LC Class. No.: QA331.7

Dewey Class. No.: 515.9

A primer on the Dirichlet space
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245 0 2 $a A primer on the Dirichlet space $h [electronic resource] / $c Omar El-Fallah ... [et al.].
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a xiii, 211 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 203
505 0 $a Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma.
520 $a 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.
650 0 $a Dirichlet principle. $3 840381
650 0 $a Hilbert space. $3 184635
650 0 $a Holomorphic functions. $3 275778
650 0 $a Functions of complex variables. $3 185972
700 1 $a El-Fallah, Omar. $3 840380
830 0 $a Cambridge tracts in mathematics ; $v 96. $3 829132
856 4 0 $u https://doi.org/10.1017/CBO9781107239425