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020 _a9781107047525
040 _aNISER LIBRARY
_beng
_cNISER LIBRARY
041 _aEnglish
082 0 4 _a517.982.22
_bEL-P
100 1 _aEl- Fallah, Omar
245 1 0 _aPrimer on the dirichlet space
260 _aCambridge :
_bCambridge University Press,
_c2014.
300 _axiii, 211p. :
_billustrations ;
_c24 cm.
490 _aCambridge tracts in mathematics ;
_v203
504 _aIncludes bibliographical references (pages 197-203) and indexes.
520 _aThe 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 _aDirichlet principle.
650 0 _aHilbert space.
650 0 _aHolomorphic functions
650 0 _aDirichlet-Raum.
650 0 _aFunctions of complex variables.
700 1 _aKellay, Karim
700 1 _aMashreghi, Javad
700 1 _aRansford, Thomas
856 _3Table of Contents
_uhttps://assets.cambridge.org/97811070/47525/toc/9781107047525_toc.pdf
856 _3Excerpt
_uhttps://assets.cambridge.org/97811070/47525/excerpt/9781107047525_excerpt.pdf
856 _3Reviews
_uhttps://www.goodreads.com/book/show/18789812-a-primer-on-the-dirichlet-space#CommunityReviews
942 _cBK
_2udc
999 _c35016
_d35016