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 potential-theoretic, but the text is self-contained
- 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 potential-theoretic, but the text is self-contained
- 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, Théorie de l'
- Polynômes
- 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 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
- 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.
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Weighted-approximation-with-varying-weight/qK8pedVIwc8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Weighted-approximation-with-varying-weight/qK8pedVIwc8/">Weighted approximation with varying weight, Vilmos Totik</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
