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Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups

In his Retiring Presidential address, delivered before the Annual Meeting of The American Mathematical Society on December, 1948, the late Professor Einar Hille spoke on his recent results on the Lie theory of semigroups of linear transformations, . . • "So far only commutative operators have b...

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Bibliographic Details
Main Authors: Jørgensen, P.E.T., Moore, R.T. (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1984, 1984
Edition:1st ed. 1984
Series:Mathematics and Its Applications
Subjects:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I: Some Main Results on Commutator Identities
  • 1. Introduction and Survey
  • 2. The Finite-Dimensional Commutation Condition
  • II: Commutation Relations and Regularity Properties for Operators in the Enveloping Algebra of Representations of Lie Groups
  • 3. Domain Regularity and Semigroup Commutation Relations
  • 4. Invariant-Domain Commutation Theory applied to the Mass-Splitting Principle
  • III: Conditions for a System of Unbounded Operators to Satisfy a given Commutation Relation
  • 5. Graph-Density applied to Resolvent Commutation, and Operational Calculus
  • 6. Graph-Density Applied to Semigroup Commutation Relations
  • 7. Construction of Globally Semigroup-invariant C?-domains
  • IV: Conditions for a Lie Algebra of Unbounded Operators to Generate a Strongly Continuous Representation of the Lie Group
  • 8. Integration of Smooth Operator Lie Algebras
  • 9. Exponentiation and Bounded Perturbation of Operator Lie Algebras
  • Appendix to Part IV
  • V: Lie Algebras of Vector Fields on Manifolds
  • 10. Applications of Commutation Theory to Vector-Field Lie Algebras and Sub- Laplacians on Manifolds
  • VI: Derivations on Modules of Unbounded Operators with Applications to Partial Differential Operators on Riemann Surfaces
  • 11. Rigorous Analysis of Some Commutator Identities for Physical Observables
  • Appendix to Part VI
  • VII: Lie Algebras of Unbounded Operators: Perturbation Theory, and Analytic Continuation of s?(2, ?)-Modules
  • 12. Exponentiation and Analytic Continuation of Heisenberg-Matrix Representations for s?(2, ?)
  • Appendix to Part VII
  • General Appendices
  • Appendix A. The Product Rule for Differentiable Operator Valued Mappings
  • Appendix B. A Review of Semigroup Folklore, and Integration in Locally Convex Spaces
  • Appendix C. The Square of an InfinitesimalGroup Generator
  • Appendix E. Compact Perturbations of Semigroups
  • Appendix G. Bounded Elements in Operator Lie Algebras
  • References
  • References to Ouotations
  • List of Symbols

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