The Resource Weighted approximation with varying weight, Vilmos Totik
Weighted approximation with varying weight, Vilmos Totik
Resource Information
The item Weighted approximation with varying weight, Vilmos Totik represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Weighted approximation with varying weight, Vilmos Totik represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 potentialtheoretic, but the text is selfcontained
 Language
 eng
 Extent
 1 online resource (vi, 114 pages)
 Contents

 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
 Isbn
 9783540483236
 Label
 Weighted approximation with varying weight
 Title
 Weighted approximation with varying weight
 Statement of responsibility
 Vilmos Totik
 Language
 eng
 Summary
 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 potentialtheoretic, but the text is selfcontained
 Action
 digitized
 Cataloging source
 SPLNM
 http://library.link/vocab/creatorName
 Totik, V
 Dewey number

 510 s
 511/.42
 Illustrations
 illustrations
 Index
 index present
 LC call number

 QA3
 QA221
 LC item number
 .L28 no. 1569
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Lecture notes in mathematics,
 Series volume
 1569
 http://library.link/vocab/subjectName

 Approximation theory
 Polynomials
 Approximation theory
 Polynomials
 Benaderingen (wiskunde)
 Polynomen
 Gewichtete Polynomapproximation
 Approximationstheorie
 Approximation, Théorie de l'
 Polynômes
 Label
 Weighted approximation with varying weight, Vilmos Totik
 Bibliography note
 Includes bibliographical references (pages 111114) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Control code
 298704332
 Dimensions
 unknown
 Extent
 1 online resource (vi, 114 pages)
 Form of item
 online
 Isbn
 9783540483236
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)298704332
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
 Label
 Weighted approximation with varying weight, Vilmos Totik
 Bibliography note
 Includes bibliographical references (pages 111114) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Control code
 298704332
 Dimensions
 unknown
 Extent
 1 online resource (vi, 114 pages)
 Form of item
 online
 Isbn
 9783540483236
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)298704332
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
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