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1、YuriA.MelnikovGreen’sFunctionsandInfiniteProductsBridgingtheDivideYuriA.MelnikovDepartmentofMathematicalSciencesComputationalSciencesProgramMiddleTennesseeStateUniversityMurfreesboro,TN37132-0001USAymelniko@mtsu.eduISBN978-0-8176-8279-8e-ISBN978-0-8176-
2、8280-4DOI10.1007/978-0-8176-8280-4SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2011937161MathematicsSubjectClassification(2010):40A20,65N80©SpringerScience+BusinessMedia,LLC2011Allrightsreserved.Thisworkmaynotbetranslatedorcopi
3、edinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieva
4、l,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionof
5、opinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.birkhauser-science.com)Tomybelovedgrandchildren:Yulya,Afanasy,andMashenkaPrefaceTwotraditionalmathematicalconcepts,classic
6、alintheirownfields,arebroughtfor-wardinthisbriefvolume.Reviewingtheseconceptsseparately,withnoconnectiontoeachother,woulddefinitelylooknatural,butbringingthemtogetherintoasinglebookformatisquiteadifferentstory.Thepointisthattheconceptsaredrawnfromsubject
7、areasofmathematicsthathavenoevidentpointsofcontiguity.Thatiswhythereadermightbeintriguedwithourintentioninthisbooktoexploretheirmutualfusion.Thisendeavorprovidesabasisforachallengingandnontrivialinvestigation.ThefirstofthetwoconceptsistheGreensfunction.
8、Itrepresentsanimportanttopicinstandardcoursesofdifferentialequationsandiscustomarilycoveredinmosttextsinthefield.Thesecondconcept,ofinfiniteproduct,belongs,inturn,toclassicalmathematicalanalysis.AstoGreen’sfunctionsforpartialdifferentiale
