Combined Measure and Shift Invariance Theory of Time Scales and Applications

Chao Wang, Ravi P. Agarwal

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English

Springer International Publishing AG
24 September 2022

Real analysis, real variables; Functional analysis & transforms; Integral calculus & equations

Series: Developments in Mathematics

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.

By: Chao Wang, Ravi P. Agarwal
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2022 ed.
Volume: 77
Dimensions: Height: 235mm, Width: 155mm,
Weight: 840g
ISBN: 9783031116186
ISBN 10: 3031116186
Series: Developments in Mathematics
Pages: 434
Publication Date: 24 September 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales.- ♢α-Measurability and Combined Measure Theory on Time Scales .- Shift Invariance and Matched Spaces of Time Scales.- Almost Periodic Functions under Matched Spaces of Time Scales.- Almost Automorphic Functions under Matched Spaces of Time Scales.- C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales.- Almost Periodic Dynamic Equations under Matched Spaces.- Almost Automorphic Dynamic Equations under Matched Spaces.- Applications on Dynamics Models under Matched Spaces.

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.

Reviews for Combined Measure and Shift Invariance Theory of Time Scales and Applications

“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)