| A Primer on the Dirichlet Space Contributor(s): El-Fallah, Omar (Author), Kellay, Karim (Author), Mashreghi, Javad (Author) |
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ISBN: 1107047528 ISBN-13: 9781107047525 Publisher: Cambridge University Press OUR PRICE: $82.64 Product Type: Hardcover - Other Formats Published: March 2014 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515.9 |
| Series: Cambridge Tracts in Mathematics (Hardcover) |
| Physical Information: 0.9" H x 6" W x 9.1" (1.00 lbs) 226 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
Contributor Bio(s): El-Fallah, Omar: - Omar El-Fallah is professor at Universit� Mohammed V-Agdal in Rabat, Morocco. He has published more than twenty research articles and has supervised eight doctoral students.Kellay, Karim: - Karim Kellay is professor at Universit� Bordeaux 1, France. He is the author of 24 research articles and has supervised three doctoral students.Mashreghi, Javad: - Javad Mashreghi is Professor of Mathematics at Universit� Laval in Qu�bec. 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. |