ComplexAnalysis:TheGeometricViewpoint,SecondEdition(CarusMathematicalMonographs)

作者 Steven G. Krantz著
出版社 TheMathematicalAssociaitonofAmerica
出版时间 2004年1月第2版
ISBN 9780883850350
定价 429.90

内容简介

Currentresearchonthespectraltheoryoffinitegraphsmaybeseenaspartofawiderefforttoforgecloserlinksbetweenalgebraandcombinatorics(inparticularbetweenlinearalgebraandgraphtheory).Thisbookdescribeshowthistopiccanbestrengthenedbyexploitingpropertiesoftheeigenspacesofadjacencymatricesassociatedwithagraph.Theextensionofspectraltechniquesproceedsatthreelevels:usingeigenvectorsassociatedwithanarbitrarylabellingofgraphvertices,usinggeometricalinvariantsofeigenspacessuchasgraphanglesandmainangles,andintroducingcertainkindsofcanonicaleigenvectorsbymeansofstarpartitionsandstarbases.Oneobjectiveistodescribegraphsbyalgebraicmeansasfaraspossible,andthebookdiscussestheUlamreconstructionconjectureandthegraphisomorphismprobleminthiscontext.Furtherproblemsofgraphreconstructionandidentificationareusedtoillustratetheimportanceofgraphanglesandstarpartitionsinrelationtographstructure.Specialistsingraphtheorywillwelcomethistreatmentofimportantnewresearch.

作者简介

StevenG.Krantz,currentlyProfessorandChairmanofMathematicsatWashingtonUniversityinSt.Louis,earnedhidPhDatPrincetonUniversityandhastaughtatUCLA,PrincetonUniversityandPennsylvaniaStateUniversity.HeistherecipientoftheUCLAAlumniFoundationDistinguishedTeachingAward,theMAA’sChauvenetPrize,theMAABeckenbachBookAward,andtheOutstandingAcademicBookAwardoftheCurrentReviewofAcademicLibraries.Hehaswrittennumerousbooksincluding:"FunctionTheoryofSeveralComplexVariables,""RealAnalysisandFoundations,TheGeometryofDomainsinSpace"(withHaroldR.Parks),"FunctionTheoryofOneComplexVariable"(withRobertE.Greene),"TheImplicitFunctionTheorem"(withHaroldParksand"APanoramaofHarmonicAnalysis"and"MathematicalApocrypha"(fortheMAA).Heisalsotheauthorofoverone-hundredresearcharticles.

— END —