Szegő's Theorem and Its Descendants : : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /

Szegő's Theorem and Its Descendants : : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / / Barry Simon.

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 tha...

Full description

Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
VerfasserIn:
Simon, Barry,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2010]
©2011
Year of Publication:2010
Edition:Course Book
Language:English
Series:Porter Lectures ; 6
Online Access:
Physical Description:1 online resource (664 p.) :; 8 line illus.
Tags: Add Tag
No Tags, Be the first to tag this record!
id 9781400837052
ctrlnum (DE-B1597)446625
(OCoLC)979579169
collection bib_alma
record_format marc
spelling Simon, Barry, author. aut http://id.loc.gov/vocabulary/relators/aut
Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / Barry Simon.
Course Book
Princeton, NJ : Princeton University Press, [2010]
©2011
1 online resource (664 p.) : 8 line illus.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Porter Lectures ; 6
Frontmatter -- Contents -- Preface -- Chapter One. Gems of Spectral Theory -- Chapter Two. Szegő's Theorem -- Chapter Three The Killip-Simon Theorem: Szegő for OPRL -- Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials -- Chapter Five. Periodic OPRL -- Chapter Six. Toda Flows and Symplectic Structures -- Chapter Seven. Right Limits -- Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL -- Chapter Nine. Szegő's Theorem for Finite Gap OPRL -- Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees -- Bibliography -- Author Index -- Subject Index
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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 polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)
MATHEMATICS Calculus.
MATHEMATICS Mathematical Analysis.
Orthogonal polynomials.
SCIENCE Physics Mathematical &amp Computational.
Spectral theory (Mathematics).
MATHEMATICS / Mathematical Analysis. bisacsh
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502
print 9780691147048
https://doi.org/10.1515/9781400837052?locatt=mode:legacy
https://www.degruyter.com/isbn/9781400837052
Cover https://www.degruyter.com/cover/covers/9781400837052.jpg
language English
format eBook
author Simon, Barry,
Simon, Barry,
spellingShingle Simon, Barry,
Simon, Barry,
Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /
Porter Lectures ;
Frontmatter --
Contents --
Preface --
Chapter One. Gems of Spectral Theory --
Chapter Two. Szegő's Theorem --
Chapter Three The Killip-Simon Theorem: Szegő for OPRL --
Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials --
Chapter Five. Periodic OPRL --
Chapter Six. Toda Flows and Symplectic Structures --
Chapter Seven. Right Limits --
Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL --
Chapter Nine. Szegő's Theorem for Finite Gap OPRL --
Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees --
Bibliography --
Author Index --
Subject Index
author_facet Simon, Barry,
Simon, Barry,
author_variant b s bs
b s bs
author_role VerfasserIn
VerfasserIn
author_sort Simon, Barry,
title Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /
title_sub Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /
title_full Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / Barry Simon.
title_fullStr Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / Barry Simon.
title_full_unstemmed Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / Barry Simon.
title_auth Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /
title_alt Frontmatter --
Contents --
Preface --
Chapter One. Gems of Spectral Theory --
Chapter Two. Szegő's Theorem --
Chapter Three The Killip-Simon Theorem: Szegő for OPRL --
Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials --
Chapter Five. Periodic OPRL --
Chapter Six. Toda Flows and Symplectic Structures --
Chapter Seven. Right Limits --
Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL --
Chapter Nine. Szegő's Theorem for Finite Gap OPRL --
Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees --
Bibliography --
Author Index --
Subject Index
title_new Szegő's Theorem and Its Descendants :
title_sort szegő's theorem and its descendants : spectral theory for l‹sup›2‹/sup› perturbations of orthogonal polynomials /
series Porter Lectures ;
series2 Porter Lectures ;
publisher Princeton University Press,
publishDate 2010
physical 1 online resource (664 p.) : 8 line illus.
Issued also in print.
edition Course Book
contents Frontmatter --
Contents --
Preface --
Chapter One. Gems of Spectral Theory --
Chapter Two. Szegő's Theorem --
Chapter Three The Killip-Simon Theorem: Szegő for OPRL --
Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials --
Chapter Five. Periodic OPRL --
Chapter Six. Toda Flows and Symplectic Structures --
Chapter Seven. Right Limits --
Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL --
Chapter Nine. Szegő's Theorem for Finite Gap OPRL --
Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees --
Bibliography --
Author Index --
Subject Index
isbn 9781400837052
9783110442502
9780691147048
callnumber-first Q - Science
callnumber-subject QC - Physics
callnumber-label QC20
callnumber-sort QC 220.7 S64 S56 42011EB
genre_facet Calculus.
Physics
url https://doi.org/10.1515/9781400837052?locatt=mode:legacy
https://www.degruyter.com/isbn/9781400837052
https://www.degruyter.com/cover/covers/9781400837052.jpg
illustrated Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 515 - Analysis
dewey-full 515/.55
dewey-sort 3515 255
dewey-raw 515/.55
dewey-search 515/.55
doi_str_mv 10.1515/9781400837052?locatt=mode:legacy
oclc_num 979579169
work_keys_str_mv AT simonbarry szegostheoremanditsdescendantsspectraltheoryforlsup2supperturbationsoforthogonalpolynomials
status_str n
ids_txt_mv (DE-B1597)446625
(OCoLC)979579169
carrierType_str_mv cr
hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
is_hierarchy_title Szegő's Theorem and Its Descendants : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /
container_title Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
_version_ 1770176646244990976
fullrecord <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04617nam a22007575i 4500</leader><controlfield tag="001">9781400837052</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20102011nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400837052</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400837052</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)446625</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)979579169</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QC20.7.S64</subfield><subfield code="b">S56 2011eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">515/.55</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 680</subfield><subfield code="2">rvk</subfield><subfield code="0">(DE-625)rvk/143252:</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Simon, Barry, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Szegő's Theorem and Its Descendants :</subfield><subfield code="b">Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials /</subfield><subfield code="c">Barry Simon.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2010]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (664 p.) :</subfield><subfield code="b">8 line illus.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Porter Lectures ;</subfield><subfield code="v">6</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Chapter One. Gems of Spectral Theory -- </subfield><subfield code="t">Chapter Two. Szegő's Theorem -- </subfield><subfield code="t">Chapter Three The Killip-Simon Theorem: Szegő for OPRL -- </subfield><subfield code="t">Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials -- </subfield><subfield code="t">Chapter Five. Periodic OPRL -- </subfield><subfield code="t">Chapter Six. Toda Flows and Symplectic Structures -- </subfield><subfield code="t">Chapter Seven. Right Limits -- </subfield><subfield code="t">Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL -- </subfield><subfield code="t">Chapter Nine. Szegő's Theorem for Finite Gap OPRL -- </subfield><subfield code="t">Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Author Index -- </subfield><subfield code="t">Subject Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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 polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">MATHEMATICS</subfield><subfield code="v">Calculus.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Orthogonal polynomials.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">SCIENCE</subfield><subfield code="v">Physics</subfield><subfield code="x">Mathematical &amp;amp</subfield><subfield code="x">Computational.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Spectral theory (Mathematics).</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="z">9783110442502</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691147048</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400837052?locatt=mode:legacy</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400837052</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/cover/covers/9781400837052.jpg</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="c">2000</subfield><subfield code="d">2013</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield></record></collection>

Similar Items