UID:
edocfu_9958085681802883
Format:
1 online resource (473 p.)
Edition:
3rd ed.
ISBN:
1-281-76334-9
,
9786611763343
,
0-08-087319-7
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; 10-II
Content:
Spectral Theory of Random Matrices
Note:
Translation of Elements d'Analyse, t.2.
,
Front Cover; Treatise on Analysis; Copyright Page; Contents; Notation; Chapter XII. Topology and Topological Algebra; 1. Topological spaces; 2. Topological concepts; 3. Hausdorff spaces; 4. Uniformizable spaces; 5. Products of uniformizable spaces; 6. Locally finite coverings and partitions of unity; 7. Semicontinuous functions; 8. Topological groups; 9. Metrizable groups; 10. Spaces with operators. orbit spaces; 11. Homogeneous spaces; 12. Quotient groups; 13. Topological vector spaces; 14. Locally convex spaces; 15. Weak topologies; 16. Baire's theorem and its consequences
,
Chapter XIII. Integration1. Definition of a measure; 2. Real measures; 3. Positive measures. The absolute value of a measure; 4. The vague topology; 5. Upper and lower integrals with respect to a positive measure; 6. Negligible functions and sets; 7. Integrable functions and sets; 8. Lebesgue's convergence theorems; 9. Measurable functions; 10. Integrals of vector-valued functions; 11. The spaces L1 and L2; 12. The space L8; 13. Measures with base μ; 14. Integration with respect to a positive measure with base μ; 15. The Lebesgue-Nikodym theorem and the order relation on MR(X)
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16. Applications: I. Integration with respect to a complex measure17. Applications: II. Dual of L1; 18. Canonical decompositions of a measure; 19. Support of a measure. Measures with compact support; 20. Bounded measures; 21. Product of measures; Chapter XIV. Integration in Locally Compact Groups; 1. Existence and uniqueness of Haar measure; 2. Particular cases and examples; 3. The modulus function on a group. The modulus of an automorphism; 4. Haar measure on a quotient group; 5. Convolution of measures on a locally compact group; 6. Examples and particular cases of convolution of measures
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7. Algebraic properties of convolution8. Convolution of a measure and a function; 9. Examples of convolutions of measures and functions; 10. Convolution of two functions; 11. Regularization; Chapter XV. Normed Algebras and Spectral Theory; 1. Normed algebras; 2. Spectrum of an element of a normed algebra; 3. Characters and spectrum of a commutative Banach algebra. The Gelfand transformation; 4. Banach algebras with involution. Star algebras; 5. Representations of algebras with involution; 6. Positive linear forms, positive Hilbert forms, and representations
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7. Traces, bitraces, and Hilbert algebras8. Complete Hilbert algebras; 9. The Plancherel-Godement theorem; 10. Representations of algebras of continuous functions; 11. The spectral theory of Hilbert; 12. Unbounded normal operators; 13. Extensions of hermitian operators; References; Index; Pure and Applied Mathematics; Erratum
,
English
Additional Edition:
ISBN 0-12-215502-5
Language:
English
