000			04146nam a22004935i 4500
003			DE-He213
005			20191011023627.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020	6	4	_a9780817644758 _9978-0-8176-4475-8
024	8	7	_a10.1007/0-8176-4475-X _2doi
050	8	4	_aQA21-27
072	8	7	_aPBX _2bicssc
072	8	7	_aMAT015000 _2bisacsh
082			_a510.9 _223
100	8	1	_aSteffens, Karl-Georg. _eauthor. _932151
245			_aThe History of Approximation Theory _h[electronic resource] : _bFrom Euler to Bernstein / _cby Karl-Georg Steffens ; edited by George A. Anastassiou.
001			000047752
300	6	4	_aXIX, 219 p. 12 illus. _bonline resource.
505	8	0	_aForerunners -- Pafnuti Lvovich Chebyshev -- The Saint Petersburg Mathematical School -- Development Outside Russia -- Constructive Function Theory: Kharkiv.
520	6	4	_aThe problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing almost exclusively algebraic methods, was headed by Chebyshev together with his coterie at the Saint Petersburg Mathematical School, while the Western mathematicians, adopting a more analytical approach, included Weierstrass, Hilbert, Klein, and others. This work traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century contributions of Sergei Bernstein in defining a new branch of function theory. One of the key strengths of this book is the narrative itself. The author combines a mathematical analysis of the subject with an engaging discussion of the differing philosophical underpinnings in approach as demonstrated by the various mathematicians. This exciting exposition integrates history, philosophy, and mathematics. While demonstrating excellent technical control of the underlying mathematics, the work is focused on essential results for the development of the theory. The exposition begins with a history of the forerunners of modern approximation theory, i.e., Euler, Laplace, and Fourier. The treatment then shifts to Chebyshev, his overall philosophy of mathematics, and the Saint Petersburg Mathematical School, stressing in particular the roles played by Zolotarev and the Markov brothers. A philosophical dialectic then unfolds, contrasting East vs. West, detailing the work of Weierstrass as well as that of the Goettingen school led by Hilbert and Klein. The final chapter emphasizes the important work of the Russian Jewish mathematician Sergei Bernstein, whose constructive proof of the Weierstrass theorem and extension of Chebyshev's work serve to unify East and West in their approaches to approximation theory. Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation.
650	8	0	_aMathematics. _98571
650	8	0	_aFourier analysis. _932152
650	8	0	_aSequences (Mathematics). _914062
650	8	0	_aMathematics_ _xHistory. _98995
650			_aMathematics. _98571
650			_aHistory of Mathematics. _98996
650			_aApproximations and Expansions. _912004
650			_aSequences, Series, Summability. _914066
650			_aFourier Analysis. _932153
700	8	1	_aAnastassiou, George A. _eeditor. _932154
710	8	2	_aSpringerLink (Online service) _932155
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9780817643539
856			_uhttp://dx.doi.org/10.1007/0-8176-4475-X _zde clik aquí para ver el libro electrónico
264	8	1	_aBoston, MA : _bBirkhuser Boston, _c2006.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c47481 _d47481
942			_c05