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Published by Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer, 1994
ISBN 10: 354057705X ISBN 13: 9783540577058
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Published by Providence, American Mathematical Society, 2006
ISBN 10: 0821839942 ISBN 13: 9780821839942
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Softcover. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. R-17293 9780821839942 Sprache: Englisch Gewicht in Gramm: 550.
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Published by New York : Springer-Verlag, 2006
ISBN 10: 038730293X ISBN 13: 9780387302935
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Published by Providence, American Math. Soc, 2014
ISBN 10: 1470416662 ISBN 13: 9781470416669
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Softcover. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00037 9781470416669 Sprache: Englisch Gewicht in Gramm: 350.
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Published by Cambridge University Press, 2012
ISBN 10: 0521135044 ISBN 13: 9780521135047
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Published by Springer Berlin Heidelberg, 1994
ISBN 10: 354057705X ISBN 13: 9783540577058
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - A new construction is given for approximating a logarithmicpotential by a discrete one. This yields a new approach toapproximation with weighted polynomials of the formw'n'(' '= uppercase)P'n'(' '= uppercase). The new techniquesettles several open problems, and it leads to a simpleproof for the strong asymptotics on some L p(uppercase)extremal problems on the real line with exponential weights,which, for the case p=2, are equivalent to power- typeasymptotics for the leading coefficients of thecorresponding orthogonal polynomials. The method is alsomodified toyield (in a sense) uniformly good approximationon the whole support. This allows one to deduce strongasymptotics in some L p(uppercase) extremal problems withvarying weights. Applications are given, relating to fastdecreasing polynomials, asymptotic behavior of orthogonalpolynomials and multipoint Pade approximation. The approachis potential-theoretic, but the text is self-contained.
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Published by Cambridge University Press, 2010
ISBN 10: 0521135044 ISBN 13: 9780521135047
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Published by Cambridge University Press CUP, 2010
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Condition: Gut. Zustand: Gut | Sprache: Englisch | Produktart: Bücher | A new construction is given for approximating a logarithmicpotential by a discrete one. This yields a new approach toapproximation with weighted polynomials of the formw"n"(" "= uppercase)P"n"(" "= uppercase). The new techniquesettles several open problems, and it leads to a simpleproof for the strong asymptotics on some L p(uppercase)extremal problems on the real line with exponential weights,which, for the case p=2, are equivalent to power- typeasymptotics for the leading coefficients of thecorresponding orthogonal polynomials. The method is alsomodified toyield (in a sense) uniformly good approximationon the whole support. This allows one to deduce strongasymptotics in some L p(uppercase) extremal problems withvarying weights. Applications are given, relating to fastdecreasing polynomials, asymptotic behavior of orthogonalpolynomials and multipoint Pade approximation. The approachis potential-theoretic, but the text is self-contained.
Language: English
Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2010
ISBN 10: 3642081738 ISBN 13: 9783642081736
Seller: AHA-BUCH GmbH, Einbeck, Germany
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the 'l/9-th' conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned 'weighted' potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.