Measure-Theoretic Calculus in Abstract Spaces: On the Playground of Infinite-Dimensional Spaces
Autor Zigang Panen Limba Engleză Hardback – 24 ian 2024
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Specificații
ISBN-13: 9783031219115
ISBN-10: 3031219112
Pagini: 933
Ilustrații: XXVII, 933 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 1.51 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Birkhäuser
Locul publicării:Cham, Switzerland
ISBN-10: 3031219112
Pagini: 933
Ilustrații: XXVII, 933 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 1.51 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Birkhäuser
Locul publicării:Cham, Switzerland
Cuprins
- 1. Introduction. - 2. Set Theory. - 3. Topological Spaces. - 4. Metric Spaces. - 5. Compact and Locally Compact Spaces. - 6. Vector Spaces. - 7. Banach Spaces. - 8. Global Theory of Optimization. - 9. Differentiation in Banach Spaces. - 10. Local Theory of Optimization. - 11. General Measure and Integration. - 12. Differentiation and Integration. - 13. Hilbert Spaces. - 14. Probability Theory.
Notă biografică
Zigang Pan was born in 1968 in Shanghai, China. He received his B.S. degree in Automatic Control from Shanghai Jiao Tong University in 1990, and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Illinois at Urbana-Champaign in 1992 and 1996, respectively. In 1996, he was a Research Engineer at the Center for Control Engineering and Computation at the University of California, Santa Barbara. In the same year, he joined the Polytechnic University, Brooklyn, NY, (now the Tandon School of Engineering at the New York University) as an Assistant Professor in the Department of Electrical Engineering for two years. Afterwards, he joined the faculty of Shanghai Jiao Tong University, Shanghai, P. R. China, in the Department of Automation. In January 2001, he joined the Department of Electrical and Computer Engineering and Computer Science of the University of Cincinnati as an Assistant Professor. Since 2005, he is pursuing research on hisown interest.
His current research interest lie in optimality-guided robust adaptive control for single-input and single-output linear systems, and its generalization to multiple-input and multiple-output systems, as well as nonlinear systems. To solidify his background knowledge in mathematics for the control theory research, he has been working on this book for sixteen years.
He was a co-winner of the 1995 George Axelby Best Paper Award of the IEEE Transaction on Automatic Control together with Professor Tamer Başar of the University of Illinois at Urbana-Champaign. He was a Silver prize winner in the 28th International Mathematical Olympiad. He is a member of the IEEE and the AMS and an affiliate of IFAC.
Textul de pe ultima copertă
This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The result of many years of the author’s careful and extensive work, this text synthesizes and builds upon the existing literature in an effort to develop and solidify the theory of measure-theoretic calculus in abstract spaces. Standard results and proofs are illustrated in general abstract settings under rigorous treatment, and numerous ancillary topics are also covered in detail, such as functional analytic treatment of optimization, probability theory, and the theory of Sobolev spaces. Applied mathematicians and researchers working in control theory, operations research, economics, optimization theory, and many other areas will find this text to be a comprehensive and invaluable resource. It can also serve as an analysis textbook for graduate-level students.
Caracteristici
Provides an encyclopedic treatment of the fundamental topics in real and functional analysis and measure theory Presents proofs of standard results in the most general abstract settings Discusses several ancillary topics, including probability theory and optimization theory