000			03703cam a22004935i 4500
001			21735852
005			20230412204821.0
006			m |o d |
007			cr |||||||||||
008			180524s2018 gw |||| o |||| 0|eng
010			_a 2019753544
020			_a978-3-319-78246-1
024	7		_a10.1007/978-3-319-78247-8 _2doi
035			_a(DE-He213)978-3-319-78247-8
040			_aDLC _beng _epn _erda _cDLC
072		7	_aMAT037000 _2bisacsh
072		7	_aPBKF _2bicssc
072		7	_aPBKF _2thema
082	0	4	_a515.7 _223
100	1		_aGarcia, Stephan Ramon, _eauthor.
245	1	0	_aFinite Blaschke Products and Their Connections / _cby Stephan Ramon Garcia, Javad Mashreghi, William T. Ross.
250			_a1st ed. 2018.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2018.
300			_a1 online resource (XIX, 328 pages 49 illustrations, 10 illustrations in color.)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Notations -- 1. Geometry of the Schur class -- 2. Elementary hyperbolic geometry -- 3. Finite Blaschke products: the basics -- 4. Approximation by finite Blaschke products -- 5. Zeros and residues -- 6. Critical points -- 7. Interpolation -- 8. The Bohr radius -- 9. Finite Blaschke products and group theory -- 10. Finite Blaschke products and operator theory -- 11. Real complex functions -- 12. Finite-dimensional model spaces -- 13. The Darlington synthesis problem -- A. Some reminders -- Index.
520			_aThis monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.
588			_aDescription based on publisher-supplied MARC data.
650		0	_aFunctional analysis.
650		0	_aOperator theory.
650	1	4	_aFunctional Analysis. _0https://scigraph.springernature.com/ontologies/product-market-codes/M12066
650	2	4	_aOperator Theory. _0https://scigraph.springernature.com/ontologies/product-market-codes/M12139
700	1		_aMashreghi, Javad, _eauthor.
700	1		_aRoss, William T, _eauthor.
776	0	8	_iPrint version: _tFinite Blaschke products and their connections. _z9783319782461 _w(DLC) 2018937693
776	0	8	_iPrinted edition: _z9783030086558
776	0	8	_iPrinted edition: _z9783319782461
776	0	8	_iPrinted edition: _z9783319782485
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
942			_2ddc _cBK _n0
999			_c4645 _d4645