000 | 02957nam a22004575i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/BFb0081880 _2doi |
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050 | 4 | _aQA299.6-433 | |
072 | 7 |
_aPBK _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBK _2thema |
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082 | 0 | 4 |
_a515 _223 |
100 | 1 |
_aAssche, Walter Van. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aAsymptotics for Orthogonal Polynomials _h[electronic resource] / _cby Walter Van Assche. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1987. |
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300 |
_aVI, 206 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1265 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0081880 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c12370 _d12370 |