Format:
1 Online-Ressource(XVI, 434 p. 2 illus.)
Edition:
1st ed. 2022.
ISBN:
9783031116193
Series Statement:
Developments in Mathematics 77
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783031116186
Additional Edition:
ISBN 9783031116209
Additional Edition:
ISBN 9783031116216
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031116186
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031116209
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031116216
Additional Edition:
Erscheint auch als Druck-Ausgabe Wang, Chao Combined measure and shift invariance theory of time scales and applications Cham, Switzerland : Springer Nature, 2022 ISBN 9783031116186
Language:
English
Keywords:
Maßkettenkalkül
;
Verschiebungsoperator
;
Invarianz
;
Fastperiodische Funktion
;
Differentialgleichung mit nacheilendem Argument
DOI:
10.1007/978-3-031-11619-3
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