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A Primer on the Dirichlet Space: Cambridge Tracts in Mathematics, cartea 203

Autor Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford
en Limba Engleză Hardback – 15 ian 2014
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.
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Specificații

ISBN-13: 9781107047525
ISBN-10: 1107047528
Pagini: 226
Ilustrații: 5 b/w illus. 110 exercises
Dimensiuni: 152 x 231 x 23 mm
Greutate: 0.45 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:New York, United States

Cuprins

Preface; 1. Basic notions; 2. Capacity; 3. Boundary behavior; 4. Zero sets; 5. Multipliers; 6. Conformal invariance; 7. Harmonically weighted Dirichlet spaces; 8. Invariant subspaces; 9. 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; References; Index of notation; Index.

Notă biografică


Descriere

The first systematic account of the Dirichlet space, one of the most fundamental Hilbert spaces of analytic functions.