Overview
- Develops a theory of combined measure and shift-invariance of time scales
- Illustrates with relevant applications to shift functions and dynamic equations
- Emphasizes the power of this theory for accurate mathematical modeling in applied sciences
Part of the book series: Developments in Mathematics (DEVM, volume 77)
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About this book
This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales.
First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains.
As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences.
Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains.
As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences.
Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
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Keywords
Table of contents (9 chapters)
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Front Matter
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Back Matter
Reviews
“The monograph is interesting and helpful for experts in the area of time scales. As an introduction to time scales and to the resulting field of dynamic equations … the original contribution due to Hilger or the textbook Dynamic equations on time scales are still strongly recommended.” (Christian Pötzsche, Mathematical Reviews, November, 2023)
Authors and Affiliations
About the authors
Chao Wang is a Professor and PhD in Mathematics at Yunnan University in China. Dr. Wang has authored the book "Theory of Translation Closedness for Time Scales" (978-3-030-38643-6), published by Springer. His research focuses on the fields of nonlinear dynamic systems, control theory, fuzzy dynamic equations, fractional differential equations, bifurcation theory, nonlinear analysis, and numerical modeling.
Ravi P. Agarwal is a Professor at the Texas A&M University-Kingsville, USA. He completed his PhD at the Indian Institute of Technology, Madras, India, in 1973. Dr. Agarwal has published 1700 research articles in several different fields and authored or co-authored 50 books, including "Theory of Translation Closedness for Time Scales" (978-3-030-38643-6), published by Springer.
Ravi P. Agarwal is a Professor at the Texas A&M University-Kingsville, USA. He completed his PhD at the Indian Institute of Technology, Madras, India, in 1973. Dr. Agarwal has published 1700 research articles in several different fields and authored or co-authored 50 books, including "Theory of Translation Closedness for Time Scales" (978-3-030-38643-6), published by Springer.
Bibliographic Information
Book Title: Combined Measure and Shift Invariance Theory of Time Scales and Applications
Authors: Chao Wang, Ravi P. Agarwal
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-031-11619-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-11618-6Published: 24 September 2022
Softcover ISBN: 978-3-031-11621-6Published: 25 September 2023
eBook ISBN: 978-3-031-11619-3Published: 22 September 2022
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XVI, 434
Number of Illustrations: 2 b/w illustrations
Topics: Functional Analysis, Analysis, Measure and Integration, Real Functions