A Primer on the Dirichlet Space
A Primer on the Dirichlet Space
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Summary
This systematic account of the Dirichlet space provides an introduction that will be valuable to researchers in function theory, assembling results previously only found in scattered research articles. Containing more than 100 exercises, the book is also suitable for self-study by graduate students in mathematics.
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A Primer on the Dirichlet Space by Omar El-Fallah
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.
Omar El-Fallah is professor at Université Mohammed V-Agdal in Rabat, Morocco. He has published more than twenty research articles and has supervised eight doctoral students. Karim Kellay is professor at Université Bordeaux 1, France. He is the author of 24 research articles and has supervised three doctoral students. Javad Mashreghi is Professor of Mathematics at Université Laval in Québec. His main fields of interest are complex analysis, operator theory and harmonic analysis. He has given numerous graduate and undergraduate courses in different institutions in English, French and Persian. Mashreghi has published several research articles, three conference proceedings, two undergraduate textbooks in French and one graduate textbook, entitled Representation Theorems for Hardy Spaces (Cambridge University Press, 2009). He was awarded the prestigious G. de B. Robinson Award of CMS (Canadian Mathematical Society), a publication award, for two long research articles in the Canadian Journal of Mathematics. Thomas Ransford is holder of a senior-level Canada Research Chair at Université Laval in Québec. His main research interests are in complex analysis, functional analysis and potential theory. He is the author of Potential Theory in the Complex Plane (Cambridge University Press, 1995) and of more than 70 research articles. He has supervised nearly 40 graduate students and postdoctoral fellows.
| SKU | Unavailable |
| ISBN 13 | 9781107047525 |
| ISBN 10 | 1107047528 |
| Title | A Primer on the Dirichlet Space |
| Author | Omar El-Fallah |
| Series | Cambridge Tracts In Mathematics |
| Condition | Unavailable |
| Publisher | Cambridge University Press |
| Year published | 2014-01-16 |
| Number of pages | 226 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |