000			02669nam a22003858i 4500
001			CR9781107239425
003			UkCbUP
005			20200124160232.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			130423s2014||||enk o ||1 0|eng|d
020			_a9781107239425 (ebook)
020			_z9781107047525 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA331.7 _b.E44 2014
082	0	4	_a515.9 _223
100	1		_aEl-Fallah, Omar, _eauthor.
245	1	2	_aA primer on the Dirichlet space / _cOmar El-Fallah [and three others].
264		1	_aCambridge : _bCambridge University Press, _c2014.
300			_a1 online resource (xiii, 211 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v203
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aPreface -- 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			_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	_aFunctions of complex variables.
776	0	8	_iPrint version: _z9781107047525
830		0	_aCambridge tracts in mathematics ; _v203.
856	4	0	_uhttps://doi.org/10.1017/CBO9781107239425
999			_c517697 _d517695