Titlebook: Combined Measure and Shift Invariance Theory of Time Scales and Applications; Chao Wang,Ravi P. Agarwal Book 2022 The Editor(s) (if applic

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Chao Wang,Ravi P. AgarwalDevelops 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 accura

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Riemann Integration, Stochastic Calculus, and Shift Operators on Time Scales,a integration on time scales are introduced including some basic results of Riemann integral and fundamental theorems of calculus. In Sect. 1.2, stochastic calculus and some basic results of stochastic dynamic equations on time scales are provided. Section 1.3 is mainly devoted to introducing the co

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Shift Invariance and Matched Spaces of Time Scales, theory of shift invariance of time scales is addressed. In Sect. 3.1, the knowledge of periodic time scales with shift operators is introduced, and some properties of shift operators are provided. In Sect. 3.2, the singularity theory of time scales under the action of the shift operators is establi

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Almost Automorphic Functions Under Matched Spaces of Time Scales,eighted pseudo .-almost automorphic functions under matched spaces is introduced and studied. In Sect. 5.2, a new generalized type of almost automorphic functions called ..-order weighted pseudo .-almost automorphic functions is firstly proposed and some of their basic properties are established. Se

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Almost Periodic Dynamic Equations Under Matched Spaces,sults of the .-almost periodic solutions and ..-order .-almost periodic solutions of a general dynamic equations are established under matched spaces of time scales. Particularly, the basic results of almost periodic problems of the .-dynamic equations on a quantum time scale are included as the spe

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Almost Automorphic Dynamic Equations Under Matched Spaces,re discussed systematically. In Sects. 8.1–8.2, the weighted pseudo .-almost automorphic solutions and the ..-order weighted pseudo .-almost automorphic solutions of the general inhomogeneous dynamic equations are studied. Moreover, In Sect. 8.3, the almost automorphy of the solutions to dynamic equ