| 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. 此书为英文版。 |
| Preface Introduction ContentscofcOthercVolumes IX: 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'sGuide X: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. ThecHilbertcspacecapproachctocclassicalcmechanics Notes Problems Reader'scGuide ListcofcSymbols Index |
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