現(xiàn)代數(shù)學(xué)物理方法（第2卷）

內(nèi)容概要

This volume continues our series of texts devoted to functional analysis methods in mathematical physics. In Volume I we announced a table of contents for Volume II. However, in the preparation of the material it became clear that we would be unable to treat the subject matter in sufficient depth in one volume. Thus, the volume contains Chapters IX and X; we expect that a third volume will appear in the near future containing the rest of the material announced as "Analysis of Operators." We hope to continue this series with an additional volume on algebraic methods.

書籍目錄

PrefaceIntroductionContentscofcOthercVolumesIX: THEFOURIERTRANSFORM  1. TheFouriertransformon(Rn)andc'(Rn),cconvolutions  2. TherangecoftheFouriertransform:Classicalspaces  3. TherangeoftheFouriertransform:Analyticity  4. LpcEstimates8a8c8ac888c888a8a8  Appendix Abstract interpolation  5. Fundamentalsolutionsofpartialdifferentialequationswithconstantcoefficients  6. Ellipticregularity  7. ThefreeHamiltonianfornonrelativisticcquantumcmechanics  8. TheGarding-Wightmancaxioms  AppendixcLorentzcinvariantmeasures   9. Restrictiontosubmanifolds   10. Productsofdistributions,wavefrontsets,andoscillatorycintegrals  Notes  Problems1  Reader'sGuideX:SELF-ADJOINTNESSANDTHEEXISTENCEOFDYNAMICS  1. Extensionsofsymmetricoperators  AppendixMotiononachalf-line,limitcpoint-limitcirclecmethods  2. Perturbationsofself-adjointoperators　3. Positivityandself-adjointnessI:cQuadraticforms　4. Positivityandself-adjointnessII:cPointwisepositivity　5. Thecommutatortheorem　6. Analyticcvectors　7. ccFreecquantumcfields　Appendix　TheWeyl　relations　for　thefree　field　8. Semigroupsandtheirgenerators　9. Hypercontractivesemigroups　10. GraphLimits　11. ThecFeynman-Kaccformula　12. Time-dependentHamiltonians　13　. Classicalnonlinearwaveequations　14. ThecHilbertcspacecapproachctocclassicalcmechanicsNotesProblemsReader'scGuideListcofcSymbolsIndex

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