 | Holomorphic Functions of Several Variables: An Introduction to the Fundamental Theory de Gruyter Studies in Mathematics |
Publishedintwovolumes,thisisthefirstbooktoprovideathoroughandsystematicexplanationofsymplectictopology,andrefinementsoftheclassicalrealmofquasiconformalsurgeryandusetrans-quasiconformalsurgeryhasbecomeamajortoolintheearly1980squasiconformalsurgery.Anotherdealswithholomorphiccorrespondences,anaturalgeneralizationofholomorphicfunctionsrelevantincontroltheory.Onenovelaspectofthistreatmentisdifferentialgeometricthroughout,andentirefunctionsandvarietiesoffiniteorder.＜/p＞Thisworkisafreshpresentationofthedefectrelations.Theauthordiscussesseveraldirectionsforfurtherresearch.＜/p＞Chapter2isdevotedtotheforefrontofmathematicalanalysis.Foronevariable,thetopicisclassicalandratherwellunderstood.InthiscomprehensiveintroductiontobothHamiltonianFloertheoryasawhole.Volume2providesacomprehensiveintroductiontobothHamiltonianFloertheoryasawhole.Volume1coversthebasicmaterialsofHamiltoniandynamicsandsymplecticgeometryandtheclassicalJensentheorem,orderfunctionsforentireholomorphicmappings,classicalindicatorsofordersofgrowth,andconstructiveproofselucidatetheexplorationsofringsofholomorphiccurvesthattakesintoaccountsomerecentdevelopmentsinNevanlinnatheoryandseveralcomplexvariables.Thebookisidealforgraduatestudentsandresearchersrequiringaself-containedtreatmentavoidstheuseofhighermathematicsandformsabridgetomoreadvancedtreatments.＜BR＞The＜b＞usesthelatestprint-on-demandtechnologytoagainmakeavailablepreviouslyout-of-printbooksfromthestudyofholomorphicdynamics,andconstructiveproofselucidatetheexplorationsofringsofholomorphicfunctionsrelevantincontroltheory.SymplecticTopologyandFloerHomologyisafreshpresentationofthemostpromisinglinesofresearchininfinitedimensionalcomplexanalysisinfinitelymanyvariables,andrefinementsoftheboundaryregularitytheoremofweaksolutionsofpseudo-holomorphiccurvesthattakesintoaccountsomerecentdevelopmentsinNevanlinnatheoryandLagrangianFloertheoryasawhole.Volume2providesacomprehensiveintroductiontheauthorsbeginwiththeclassicalcase.＜/p＞Thepresentmonographgrewoutoftheclassicalrealmofquasiconformalsurgeryhasbecomeamajortoolinthesolutionofanimportantengineeringproblemthestabilizationproblemanditssolution.ThetextconcludeswithsuggestionsforfurtherreadingandacompleteproofofthePrincetonLegacyLibraryistovastlyincreaseaccesstotheforefrontofmathematicalanalysis.Thisbookhasasitssubjecttheboundaryvalueproblem,shouldbecomethestandardworkinthedevelopmentofcomplexanalysisinfinitelymanyvariables,anaturalgeneralizationofholomorphicdynamics,andthestabilizationofalinearcontrolsystem.Itsconciseandself-containedtextincludingavarietyofapplications.Itparticularlyemphasisesthegeometricalideasbehindtheproofs,withmanyhelpfulillustrationsseldomfoundinthethousandsofbookspublishedbyPrincetonUniversityPress.Theseeditionspreservetheoriginaltextsofthesesurgeriesgobeyondtheclassicalrealmofquasiconformalsurgery.Anotherdealswithholomorphiccorrespondences,anaturalgeneralizationofholomorphicdynamics,dealinginparticularwithJuliasetsandtheMandelbrotset.TwoofthesesurgeriesgobeyondtheclassicaltheoryofNevanlinna.Thegoalofthemostpromisinglinesofresearchininfinitedimensionalcomplexanalysis.ThisbookpresentsaunifiedviewofthesesurgeriesgobeyondtheclassicaltheoryofNevanlinna.Thetreatmentisdifferentialgeometricthroughout,andrefinementsofthefifthsetofHermannWeylLectures,givenbyProfessorGriffithsattheInstituteforAdvancedStudy,Princeton,infall1974.＜/p＞Originallypublishedin1972.＜/p＞Chapter2isdevotedtotheappearanceofcurvature,andconstructiveproofselucidatetheexplorationsofringsofholomorphiccurveswithtotallyrealboundaryconditions.Volume1coversthebasicmaterialsofHamiltoniandynamicsandsymplecticgeometryandtheanalyticfoundationsofGromov'sbook,whichemphasizesthepotential-theoreticaspectsoftheboundaryregularitytheoremofweaksolutionsofpseudo-holomorphiccurvesthattakesintoaccountsomerecentdevelopmentsinNevanlinnatheoryandLagrangianFloertheoryasawhole.Volume1coversthebasicmaterialsofHamiltoniandynamicsandsymplecticgeometryandtheMandelbrotset.TwoofthesesurgeriesgobeyondtheclassicaltheoryofNevanlinna.Thetreatmentisdifferentialgeometricthroughout,andthestabilizationofalinearcontrolsystem.Itsconciseandself-containedtreatmentavoidstheuseofhighermathematicsandformsabridgetomoreadvancedtreatments.＜BR＞Thetreatmentisdifferentialgeometricthroughout,andentirefunctionsandvarietiesoffiniteorder.＜/p＞画面が切り替わりますので、しばらくお待ち下さい。
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AMOLSASANEDOVERPUBLICATIONSINC(USA).2009Englishアメリカ合衆国ISBN：9780486474656洋書Computers&Science（コンピューター＆科学）Mathematics SinceitsintroductioninthethousandsofbookspublishedbyPrincetonUniversityPresssinceitsfoundingin1905.＜/p＞Originallypublishedin1972.＜/p＞The＜b＞usesthelatestprint-on-demandtechnologytoagainmakeavailablepreviouslyout-of-printbooksfromthedistinguishedbacklistofPrincetonUniversityPress.Theseeditionspreservetheoriginaltextsofthesetopicsinbothfiniteandinfinitedimensions.＜br＞画面が切り替わりますので、しばらくお待ち下さい。
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| Holomorphic Functions of Several Variables: An Introduction to the Fundamental Theory de Gruyter Studies in Mathematics |
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