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Published in:
2022 | OriginalPaper | Chapter
Nonstandard Analysis of Almost Periodicity
Authors : S. Alagu, R. Kala
Published in: Mathematical, Computational Intelligence and Engineering Approaches for Tourism, Agriculture and Healthcare
Publisher: Springer Singapore
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Abstract
Nonstandard Analysis was introduced by Abraham Robinson in 1966 and Edward Nelson gave an axiomatic approach to it in 1977. The advantages of nonstandard analytic viewpoint are manyfold. To name a few, one is that it gives a natural insight into mathematical structures; another is that it reduces infiniteness to finiteness and infinitesimals to concrete objects.
Many a time, we try to study mathematical entities by approximating them by elementary objects. For example, we try to approximate continuous functions by polynomials. Almost periodicity is a study of approximating functions on locally compact abelian groups by trigonometric polynomials. In [9], the notion of Almost periodicity is carried out for operators also. In this paper, we nonstandardized Almost periodicity for the ‘traditional’ functions and then finally for the operators too.