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- catalog abstract "A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof 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- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.".
- catalog contributor b5883388.
- catalog created "c1994.".
- catalog date "1994".
- catalog date "c1994.".
- catalog dateCopyrighted "c1994.".
- catalog description "1. Introduction -- I. Freud weights. 2. Short proof for the approximation problem for Freud weights. 3. Strong asymptotics -- II. Approximation with general weights. 4. A general approximation theorem. 5. Preliminaries to the proofs. 6. Proof of Theorems 4.1, 4.2 and 4.3. 7. Construction of Examples 4.5 and 4.6 -- III. Varying weights. 8. Uniform approximation by weighted polynomials with varying weights. 9. Modification of the method. 10. Approximation in geometric means -- IV. Applications. 11. Fast decreasing polynomials. 12. Approximation by W(a[subscript n]x)P[subscript n](x). 13. Extremal problems with varying weights. 14. Asymptotic properties of orthogonal polynomials with varying weights. 15. Freud weights revisited. 16. Multipoint Pade approximation -- 17. Concluding remarks.".
- catalog description "A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof 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- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.".
- catalog description "Includes bibliographical references (p. - ) and index.".
- catalog extent "vi, 114 p. ;".
- catalog hasFormat "Weighted approximation with varying weight.".
- catalog identifier "038757705X (New York : acid-free) :".
- catalog identifier "354057705X (Berlin : softcover : acid-free)".
- catalog isFormatOf "Weighted approximation with varying weight.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1569.".
- catalog isPartOf "Lecture notes in mathematics ; 1569".
- catalog issued "1994".
- catalog issued "c1994.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Weighted approximation with varying weight.".
- catalog subject "510 s 511/.42 20".
- catalog subject "Approximation theory.".
- catalog subject "Polynomials.".
- catalog subject "QA3 .L28 no. 1569 QA221".
- catalog tableOfContents "1. Introduction -- I. Freud weights. 2. Short proof for the approximation problem for Freud weights. 3. Strong asymptotics -- II. Approximation with general weights. 4. A general approximation theorem. 5. Preliminaries to the proofs. 6. Proof of Theorems 4.1, 4.2 and 4.3. 7. Construction of Examples 4.5 and 4.6 -- III. Varying weights. 8. Uniform approximation by weighted polynomials with varying weights. 9. Modification of the method. 10. Approximation in geometric means -- IV. Applications. 11. Fast decreasing polynomials. 12. Approximation by W(a[subscript n]x)P[subscript n](x). 13. Extremal problems with varying weights. 14. Asymptotic properties of orthogonal polynomials with varying weights. 15. Freud weights revisited. 16. Multipoint Pade approximation -- 17. Concluding remarks.".
- catalog title "Weighted approximation with varying weights / Vilmos Totik.".
- catalog type "text".