Coverart for item
The Resource Weighted approximation with varying weight, Vilmos Totik

Weighted approximation with varying weight, Vilmos Totik

Label
Weighted approximation with varying weight
Title
Weighted approximation with varying weight
Statement of responsibility
Vilmos Totik
Creator
Subject
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 potential-theoretic, but the text is self-contained
Member of
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
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 111-114) 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
Publication
Bibliography note
Includes bibliographical references (pages 111-114) 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.

Library Locations

    • Ellis LibraryBorrow it
      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012
Processing Feedback ...