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001 978-3-540-47711-2
003 DE-He213
005 20190213151929.0
007 cr nn 008mamaa
008 121227s1987 gw | s |||| 0|eng d
020 _a9783540477112
_9978-3-540-47711-2
024 7 _a10.1007/BFb0081880
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aAssche, Walter Van.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAsymptotics for Orthogonal Polynomials
_h[electronic resource] /
_cby Walter Van Assche.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1987.
300 _aVI, 206 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1265
505 0 _aOrthogonal polynomials on a compact set -- Asymptotically periodic recurrence coefficients -- Probabilistic proofs of asymptotic formulas -- Orthogonal polynomials on unbounded sets -- Zero distribution and consequences -- Some applications.
520 _aRecently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540180234
776 0 8 _iPrinted edition:
_z9783662175545
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1265
856 4 0 _uhttps://doi.org/10.1007/BFb0081880
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12370
_d12370