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Functional Analysis - Jan Van Neerven

Functional Analysis

(Autor)

Buch | Softcover
726 Seiten
2024
Cambridge University Press (Verlag)
978-1-009-54246-3 (ISBN)
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This comprehensive introduction to functional analysis covers both the abstract theory and applications. With carefully written out proofs, more than 300 problems, and appendices covering prerequisites, this self-contained volume can be used as a text for a graduate-level course and as a reference text for researchers in the field.
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.

Jan van Neerven holds an Antoni van Leeuwenhoek professorship at Delft University of Technology. Author of four books and more than 100 peer-reviewed articles, he is a leading expert in functional analysis and operator theory and their applications in stochastic analysis and the theory of partial differential equations.

1. Banach spaces; 2. The classical Banach spaces; 3. Hilbert spaces; 4. Duality; 5. Bounded operators; 6. Spectral theory; 7. Compact operators; 8. Bounded operators on Hilbert spaces; 9. The spectral theorem for bounded normal operators; 10. The spectral theorem for unbounded normal operators; 11. Boundary value problems; 12. Forms; 13. Semigroups of linear operators; 14. Trace class operators; 15. States and observables; Appendix A. Zorn's lemma; Appendix B. Tensor products; Appendix C. Topological spaces; Appendix D. Metric spaces; Appendix E. Measure spaces; Appendix F. Integration; Appendix G. Notes; References; Index.

Erscheinungsdatum
Reihe/Serie Cambridge Studies in Advanced Mathematics
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Gewicht 1161 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie
ISBN-10 1-009-54246-X / 100954246X
ISBN-13 978-1-009-54246-3 / 9781009542463
Zustand Neuware
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