teschl g. jacobi operators and completely integrable nonlinear lattices (ams surveys and monographs 72)(369s)

《teschl g. jacobi operators and completely integrable nonlinear lattices (ams surveys and monographs 72)(369s)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MathematicalSurveysandMonographsVolume72JacobiOperatorsandCompletelyIntegrableNonlinearLatticesGeraldTeschlUniversityofViennaAmericanMathematicalSocietyEditorialBoardGeorgiaM.BenkartMichaelLossPeterLandweberTudorStefanRatiu,Chair1991Mathematicssubjectclassification.39Axx,47B39,58F07Abstract.T

2、hisbookisintendedtoservebothasanintroductionandareferencetospectralandinversespectraltheoryofJacobioperators(i.e.,secondordersymmetricdifferenceoperators)andapplicationsofthesetheoriestotheTodaandKac-vanMoerbekehierarchy.Startingfromsecondorderdifferenceequationswemoveontoself-adjointoperators

3、anddevelopdiscreteWeyl-Titchmarsh-Kodairatheory,coveringallclassicalaspectslikeWeylm-functions,spectralfunctions,themomentproblem,inversespectraltheory,anduniquenessresults.Next,weinvestigatesomemoreadvancedtopicslikelocatingtheessential,absolutelycontinuous,anddiscretespectrum,subordinacy,o

4、scillationtheory,traceformulas,randomoperators,almostperiodicoperators,(quasi-)periodicoperators,scatteringtheory,andspectraldeformations.Then,theLaxapproachisusedtointroducetheTodahierarchyanditsmodifiedcounterpart,theKac-vanMoerbekehierarchy.Uniquenessandexistencetheoremsfortheinitialvaluep

5、roblem,solutionsintermsofRiemannthetafunctions,theinversescatteringtransform,B¨acklundtransformations,andsolitonsolutionsarediscussed.Correctionsandcomplementstothisbookareavailablefrom:http://www.mat.univie.ac.at/˜gerald/ftp/book-jac/TypesetbyAMS-LATEX,PicTEX,andMakeindex.Version:June7,2004

6、.LibraryofCongressCataloging-in-PublicationDataTeschl,Gerald,1970–JacobiOperatorsandCompletelyIntegrableNonlinearLattices/GeraldTeschl.p.cm.—(Mathematicalsurveysandmonographs,ISSN0076-5376;V.72)Includesbibliographicalreferencesandindex.ISBN0-8218-1940-21.Jacobioperators.2.Differentiabledynami

7、calsystems.I.Title.II.Series:Math-emticalsurveysandmonographs;no.72.QA329.2.T47199999-39165515’.7242–dc21CIPCopyingandreprinting.Individualreadersofthispublication,andnonprofitlibrariesactingforthem,arepermittedtomakefairuseofthematerial,suchastocop