Author | Segal, Irving E. author |
---|---|
Title | Integrals and Operators [electronic resource] / by Irving E. Segal, Ray A. Kunze |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1978 |
Edition | Second Revised and Enlarged Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-66693-3 |
Descript | XIV, 374 p. online resource |
I. Introduction -- 1.1 General preliminaries -- 1.2 The idea of measure -- 1.3 Integration as a technique in analysis -- 1.4 Limitations on the concept of measure space -- 1.5 Generalized spectral theory and measure spaces -- Exercises -- II. Basic Integrals -- 2.1 Basic measure spaces -- 2.2 The basic Lebesgue-Stieltjes spaces -- Exercises -- 2.3 Integrals of step functions -- Exercises -- 2.4 Products of basic spaces -- 2.5* Coin-tossing space -- Exercises -- 2.6 Infinity in integration theory -- Exercises -- III. Measurable Functions and Their Integrals -- 3.1 The extension problem -- 3.2 Measurability relative to a basic ring -- Exercises -- 3.3 The integral -- Exercises -- 3.4 Development of the integral -- Exercises -- 3.5 Extensions and completions of measure spaces -- Exercises -- 3.6 Multiple integration -- Exercises -- 3.7 Large spaces -- Exercises -- IV. Convergence and Differentiation -- 4.1 Linear spaces of measurable functions -- Exercises -- 4.2 Set functions -- Exercises -- 4.3 Differentiation of set functions -- Exercises -- V. Locally Compact and Euclidean Spaces -- 5.1 Functions on locally compact spaces -- Exercises -- 5.2 Measures in locally compact spaces -- Exercises -- 5.3 Transformation of Lebesgue measure -- Exercises -- 5.4 Set functions and differentiation in euclidean space -- Exercises -- VI. Function Spaces -- 6.1 Linear duality 152 Exercises -- Exercises -- 6.2 Vector-valued functions -- Exercises -- VII. Invariant Integrals -- 7.1 Introduction -- 7.2 Transformation groups -- Exercises -- 7.3 Uniform spaces -- Exercises -- 7.4 The Haar integral -- 7.5 Developments from uniqueness -- Exercises -- 7.6 Function spaces under group action -- Exercises -- VIII. Algebraic Integration Theory -- 8.1 Introduction -- 8.2 Banach algebras and the characterization of function algebras -- Exercises -- 8.3 Introductory features of Hilbert spaces -- Exercises -- 8.4 Integration algebras -- Exercises -- IX. Spectral Analysis in Hilbert Space -- 9.1 Introduction -- 9.2 The structure of maximal Abelian self-adjoint algebras -- Exercises -- X. Group Representations and Unbounded Operators -- 10.1 Representations of locally compact groups -- 10.2 Representations of Abelian groups -- Exercises -- 10.3 Unbounded diagonalizable operators -- Exercises -- 10.4 Abelian harmonic analysis -- Exercises -- XI. Semigroups and Perturbation Theory -- 11.1 Introduction -- 11.2 The Hille-Yosida theorem -- 11.3 Convergence of semigroups -- 11.4 Strong convergence of self-adjoint operators -- 11.5 Rellich-Kato perturbations -- Exercises -- 11.6 Perturbations in a calibrated space -- Exercises -- XII. Operator Rings and Spectral Multiplicity -- 12.1 Introduction -- 12.2 The double-commutor theorem -- Exercises -- 12.3 The structure of abelian rings -- Exercises -- XIII. C*-Algebras and Applications -- 13.1 Introduction -- 13.2 Representations and states -- Exercises -- XIV. The Trace as a Non-Commutative Integral -- 14.1 Introduction -- 14.2 Elementary operators and the trace -- Exercises -- 14.3 Hilbert algebras -- Exercises -- Selected references