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THE CONNECTION BETWEEN PSEUDO ALMOST PERIODIC FUNCTIONS DEFINED ON TIME SCALES AND ON THE REAL LINE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 3 / June 2017
- Published online by Cambridge University Press:
- 22 February 2017, pp. 482-494
- Print publication:
- June 2017
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- Article
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- You have access
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A necessary and sufficient condition for a continuous function
$g$ to be almost periodic on time scales is the existence of an almost periodic function 
$f$ on 
$\mathbb{R}$ such that 
$f$ is an extension of 
$g$. Our aim is to study this question for pseudo almost periodic functions. We prove the necessity of the condition for pseudo almost periodic functions. An example is given to show that the sufficiency of the condition does not hold for pseudo almost periodic functions. Nevertheless, the sufficiency is valid for uniformly continuous pseudo almost periodic functions. As applications, we give some results on the connection between the pseudo almost periodic (or almost periodic) solutions of dynamic equations on time scales and of the corresponding differential equations.
