عنوان

Operator Commutation Relations :

شابک

9400963289

شابک

9789400963283

شماره

b593662

عنوان اصلي

Operator Commutation Relations :

نام عام مواد

[Book]

ساير اطلاعات عنواني

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

نام نخستين پديدآور

by Palle E.T. Jørgensen, Robert T. Moore.

محل نشرو پخش و غیره

Dordrecht

نام ناشر، پخش کننده و غيره

Springer Netherlands

تاریخ نشرو بخش و غیره

1984

نام خاص و کميت اثر

(511 pages).

عنوان فروست

Mathematics and Its Applications, 14.

متن يادداشت

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 Infinitesimal Group Generator --; Appendix E. Compact Perturbations of Semigroups --; Appendix G. Bounded Elements in Operator Lie Algebras --; References --; References to Ouotations --; List of Symbols.

متن يادداشت

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 been considered and the product law ... is the simplest possible. The non-commutative case has resisted numerous attacks in the past and it is only a few months ago that any headway was made with this problem. I shall have the pleasure of outlining the new theory here; it is a blend of the classical theory of Lie groups with the recent theory of one-parameter semigroups." The list of references in the subsequent publication of Hille's address (Bull. Amer. Math -. Soc. 56 (1950)) includes pioneering papers of I.E. Segal, I.M. Gelfand, and K. Yosida. In the following three decades the subject grew tremendously in vitality, incorporating a number of different fields of mathematical analysis. Early papers of V. Bargmann, I.E. Segal, L. G~ding, Harish-Chandra, I.M. Singer, R. Langlands, B. Konstant, and E. Nelson developed the theoretical basis for later work in a variety of different applications: Mathematical physics, astronomy, partial differential equations, operator algebras, dynamical systems, geometry, and, most recently, stochastic filtering theory. As it turned out, of course, the Lie groups, rather than the semigroups, provided the focus of attention.

موضوع مستند نشده

Global analysis (Mathematics)

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Palle E.T. Jørgensen, Robert T. Moore.

مستند نام اشخاص تاييد نشده

Palle E T Jørgensen

مستند نام اشخاص تاييد نشده

Robert T Moore

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y