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 authors 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.
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Product Details
Weight: 1604g
Dimensions: 155 x 235mm
Publication Date: 24 Jan 2024
Publisher: Birkhauser Verlag AG
Publication City/Country: Switzerland
Language: English
ISBN13: 9783031219115
About Zigang Pan
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 Baar 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.