Measure-Theoretic Calculus in Abstract Spaces

On the Playground of Infinite-Dimensional Spaces

Zigang Pan (Autor)

Buch | Hardcover

XXVII, 933 Seiten

2024 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-21911-5 (ISBN)

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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.

lt;b>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 his own 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 Basar 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.

- 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.

Erscheinungsdatum	25.01.2024
Zusatzinfo	XXVII, 933 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1604 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik ► Elektrotechnik / Energietechnik
Schlagworte	Banach Space of Measures • Banach Space Valued Measure • Bounded Convergence Theorem • Change of Variable Between Measure Spaces • General Integration Theory • Hahn-Banach theorem • infinite-dimensional spaces • Lebesgue Dominated Convergence Theorem • Mapping Theorems • Measure Theoretic Calculus • measure theory • Mode of Convergence • Optimization by Vector Space Method • Sobolev Space
ISBN-10	3-031-21911-2 / 3031219112
ISBN-13	978-3-031-21911-5 / 9783031219115
Zustand	Neuware