Szegő's theorem and its descendants :: spectral theory for L2 perturbations of orthogonal polynomials /
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background th...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J. :
Princeton University Press,
©2011.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomia. |
| Beschreibung: | 1 online resource (x, 650 pages) |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9781400837052 1400837057 1282821156 9781282821156 |
Internformat
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| 245 | 1 | 0 | |a Szegő's theorem and its descendants : |b spectral theory for L2 perturbations of orthogonal polynomials / |c Barry Simon. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c ©2011. | ||
| 300 | |a 1 online resource (x, 650 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references and indexes. | ||
| 520 | |a This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomia. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Contents; Preface; Chapter 1. Gems of Spectral Theory; Chapter 2. Szego's Theorem; Chapter 3. The Killip-Simon Theorem: Szego for OPRL; Chapter 4. Sum Rules and Consequences for Matrix Orthogonal Polynomials; Chapter 5. Periodic OPRL; Chapter 6. Toda Flows and Symplectic Structures; Chapter 7. Right Limits; Chapter 8. Szego and Killip-Simon Theorems for Periodic OPRL; Chapter 9. Szego's Theorem for Finite Gap OPRL; Chapter 10. A.C. Spectrum for Bethe-Cayley Trees; Bibliography; Author Index; Subject Index. | |
| 650 | 0 | |a Spectral theory (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85126408 | |
| 650 | 0 | |a Orthogonal polynomials. |0 http://id.loc.gov/authorities/subjects/sh85095794 | |
| 650 | 6 | |a Spectre (Mathématiques) | |
| 650 | 6 | |a Polynômes orthogonaux. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Physics |x Mathematical & Computational. |2 bisacsh | |
| 650 | 7 | |a Orthogonal polynomials |2 fast | |
| 650 | 7 | |a Spectral theory (Mathematics) |2 fast | |
| 758 | |i has work: |a Szegő's theorem and its descendants (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH399xvM37YtyQ7rcWxybb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| author | Simon, Barry, 1946- |
| author_GND | http://id.loc.gov/authorities/names/n79082366 |
| author_facet | Simon, Barry, 1946- |
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| author_sort | Simon, Barry, 1946- |
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| callnumber-sort | QC 220.7 S64 S56 42011EB |
| callnumber-subject | QC - Physics |
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| collection | ZDB-4-EBA |
| contents | Cover; Contents; Preface; Chapter 1. Gems of Spectral Theory; Chapter 2. Szego's Theorem; Chapter 3. The Killip-Simon Theorem: Szego for OPRL; Chapter 4. Sum Rules and Consequences for Matrix Orthogonal Polynomials; Chapter 5. Periodic OPRL; Chapter 6. Toda Flows and Symplectic Structures; Chapter 7. Right Limits; Chapter 8. Szego and Killip-Simon Theorems for Periodic OPRL; Chapter 9. Szego's Theorem for Finite Gap OPRL; Chapter 10. A.C. Spectrum for Bethe-Cayley Trees; Bibliography; Author Index; Subject Index. |
| ctrlnum | (OCoLC)677162060 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:17:35Z |
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| publisher | Princeton University Press, |
| record_format | marc |
| spelling | Simon, Barry, 1946- https://id.oclc.org/worldcat/entity/E39PBJbMcCjJtptX9HCWtTTmBP http://id.loc.gov/authorities/names/n79082366 Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / Barry Simon. Princeton, N.J. : Princeton University Press, ©2011. 1 online resource (x, 650 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and indexes. This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomia. Print version record. Cover; Contents; Preface; Chapter 1. Gems of Spectral Theory; Chapter 2. Szego's Theorem; Chapter 3. The Killip-Simon Theorem: Szego for OPRL; Chapter 4. Sum Rules and Consequences for Matrix Orthogonal Polynomials; Chapter 5. Periodic OPRL; Chapter 6. Toda Flows and Symplectic Structures; Chapter 7. Right Limits; Chapter 8. Szego and Killip-Simon Theorems for Periodic OPRL; Chapter 9. Szego's Theorem for Finite Gap OPRL; Chapter 10. A.C. Spectrum for Bethe-Cayley Trees; Bibliography; Author Index; Subject Index. Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Spectre (Mathématiques) Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh SCIENCE Physics Mathematical & Computational. bisacsh Orthogonal polynomials fast Spectral theory (Mathematics) fast has work: Szegő's theorem and its descendants (Text) https://id.oclc.org/worldcat/entity/E39PCH399xvM37YtyQ7rcWxybb https://id.oclc.org/worldcat/ontology/hasWork Print version: Simon, Barry, 1946- Szegö's theorem and its descendants. Princeton, N.J. : Princeton University Press, ©2011 9780691147048 (DLC) 2010023223 (OCoLC)587249070 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340202 Volltext |
| spellingShingle | Simon, Barry, 1946- Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / Cover; Contents; Preface; Chapter 1. Gems of Spectral Theory; Chapter 2. Szego's Theorem; Chapter 3. The Killip-Simon Theorem: Szego for OPRL; Chapter 4. Sum Rules and Consequences for Matrix Orthogonal Polynomials; Chapter 5. Periodic OPRL; Chapter 6. Toda Flows and Symplectic Structures; Chapter 7. Right Limits; Chapter 8. Szego and Killip-Simon Theorems for Periodic OPRL; Chapter 9. Szego's Theorem for Finite Gap OPRL; Chapter 10. A.C. Spectrum for Bethe-Cayley Trees; Bibliography; Author Index; Subject Index. Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Spectre (Mathématiques) Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh SCIENCE Physics Mathematical & Computational. bisacsh Orthogonal polynomials fast Spectral theory (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85126408 http://id.loc.gov/authorities/subjects/sh85095794 |
| title | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / |
| title_auth | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / |
| title_exact_search | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / |
| title_full | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / Barry Simon. |
| title_fullStr | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / Barry Simon. |
| title_full_unstemmed | Szegő's theorem and its descendants : spectral theory for L2 perturbations of orthogonal polynomials / Barry Simon. |
| title_short | Szegő's theorem and its descendants : |
| title_sort | szego s theorem and its descendants spectral theory for l2 perturbations of orthogonal polynomials |
| title_sub | spectral theory for L2 perturbations of orthogonal polynomials / |
| topic | Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Spectre (Mathématiques) Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh SCIENCE Physics Mathematical & Computational. bisacsh Orthogonal polynomials fast Spectral theory (Mathematics) fast |
| topic_facet | Spectral theory (Mathematics) Orthogonal polynomials. Spectre (Mathématiques) Polynômes orthogonaux. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. SCIENCE Physics Mathematical & Computational. Orthogonal polynomials |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340202 |
| work_keys_str_mv | AT simonbarry szegostheoremanditsdescendantsspectraltheoryforl2perturbationsoforthogonalpolynomials |