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Indeholder "Preface", "Introduction", "I. Preliminaries", " 1. Sets and functions", " 2. Metric and normed linear spaces", " Appendix. Lim sup and lim inf", " 3. The Lebesgue integral", " 4. Abstract measure theory", " 5. Two convergence arguments", " 6. Equicontinuity", " Notes", " Problems", "II.
Første bind af fire med noget af matematikken bag den moderne fysik.
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Hilbert Spaces", " 1. The geometry of Hilbert space", " 2. The Riesz lemma", " 3. Orthonormal bases", " 4. Tensor products of Hilbert spaces", " 5. Ergodic theory: an introduction", " Notes", " Problems", "III. Banach Spaces", " 1. Definition and examples", " 2. Duals and double duals", " 3. The Hahn-Banach theorem", " 4. Operations on Banach spaces", " 5. The Baire category theorem and its consequences", " Notes", " Problems", "IV. Topological Spaces", " 1. General notions", " 2. Nets and convergence", " 3. Compactness", " Appendix. The Stone-Weierstrass theorem", " 4. Measure theory on compact spaces", " Appendix. Weak and strong measurability", " Notes", " Problems", "V. Locally Convex Spaces", " 1. General properties", " 2. Fréchet spaces", " 3. Functions of rapid decrease and the tempered distributions", " Appendix. The N-representation for L and L'", " 4. Inductive limits: generalized functions and weak solutions of partial differential equations", " 5. Fixed point theorems", " 6. Applications of fixed point theorems", " 7. Topologies on locally convex spaces: duality theory and the strong dual topology", " Appendix. Polars and the Mackey-Arens theorem", " Notes", " Problems", "VI. Bounded Operators", " 1. Topologies on bounded operators", " 2. Adjoints", " 3. The spectrum", " 4. Positive operators and the polar decomposition", " 5. Compact operators", " 6. The trace class and Hilbert-Schmidt ideals", " Notes", " Problems", "VII. The Spectral Theorem", " 1. The continuous functional calculus", " 2. The spectral measures", " 3. Spectral projections", " 4. Ergodic theory revisited: Koopmanism", " Notes", " Problems", "VIII. Unbounded Operators", " 1. Domains, graphs, adjoints, and spectrum", " 2. Symmetry and self-adjoint operators: the basic criterion for self-adjointness", " 3. The spectral theorem", " 4. Stone's theorem", " 5. Formal manipulation is a touchy business: Nelson's example", " 6. Quadratic forms", " 7. Convergence of unbounded operators", " 8. The Trotter product formula", " 9. The polar decomposition for closed operators", " 10. Tensor products", " 11. Three mathematical problems in quantum mechanics", " Notes", " Problems", "The Fourier Transform", " 1. The Fourier Transform om L(R^n) and L'(R^n), convolutions", " 2. The range of tFourier transform: Classical spaces", " 3. The range of tFourier transform: Analyticity", " Notes", " Problems", "Supplementary Material", " II.2 Applications of the Riesz lemma", " III.1 Basic properties of L^p spaces", " IV.3 Proof of Tychonoff's theorem", " IV.4 The Riesz-Markov theorem for X = [0,1]", " IV.5 Minimization of functionals", " V.5 Proofs of some theorems in nonlinear functional analysis", " VI.5 Applications of compact operators", " VIII.7 Monotone convergence for forms", " VIII.8 More on the Trotter product formula", " Uses of the maximum principle", " Notes", " Problems", "List of Symbols", "Index".Første bind af fire med noget af matematikken bag den moderne fysik.
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Publication
Academic Press (1981), Edition: 2Rev Ed, Hardcover, 400 pages
Description
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
Language
Original language
English
Physical description
400 p.; 23 cm
ISBN
0125850506 / 9780125850506
Local notes
Omslag: Ikke angivet
Omslaget viser titel og forfatternavn
Indskannet omslag - N650U - 150 dpi
Side xii: decease (typo for decrease)
Side 1: The beginner ... should not be discouraged if ... he finds that he does not have the prerequisites for reading the prerequisites. -- P. Halmos
Omslaget viser titel og forfatternavn
Indskannet omslag - N650U - 150 dpi
Side xii: decease (typo for decrease)
Side 1: The beginner ... should not be discouraged if ... he finds that he does not have the prerequisites for reading the prerequisites. -- P. Halmos
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Pages
400
DDC/MDS
| 530.15 |