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Combined measure and shift invarianc...

Wang, Chao.

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Combined measure and shift invariance theory of time scales and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Combined measure and shift invariance theory of time scales and applications/ by Chao Wang, Ravi P. Agarwal.
Author:	Wang, Chao.
other author:	Agarwal, Ravi P.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xvi, 434 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Measure theory. -
Online resource:	https://doi.org/10.1007/978-3-031-11619-3
ISBN:	9783031116193

Combined measure and shift invariance theory of time scales and applications
Wang, Chao.

Combined measure and shift invariance theory of time scales and applications[electronic resource] /by Chao Wang, Ravi P. Agarwal. - Cham :Springer International Publishing :2022. - xvi, 434 p. :ill., digital ;24 cm. - Developments in mathematics,v. 772197-795X ;. - Developments in mathematics ;v. 77..

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.

ISBN: 9783031116193

Standard No.: 10.1007/978-3-031-11619-3doiSubjects--Topical Terms:

516951
Measure theory.

LC Class. No.: QA312 / .W35 2022

Dewey Class. No.: 515.42

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520 $a 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.
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