Some algebraic and topological structures of Fourier transformable functions

Document Type : Original Article

Authors

1 Department of Mathematics, University of Balochistan, Quetta, 87300, Pakistan

2 Department of Mathematics, Hamedan Branch, Islamic Azad University,Hamedan, Iran

3 Department of Baic Sciences, Mehran University of Engineering and Technology, Jamshoro, Pakistan

Abstract

In this work, the set of all functions that are Fourier transformable with regard to their structure both algebraic and topological is taken into account. Certain topological properties of the set of Fourier transformable functions with the help of a metric are described. Also determines the proofs of the statements that the set of all Fourier transformable functions is a commutative semi-group with respect to the convolution operation as well as Abelian group with respect to the operation of addition. Metric for two functions belonging to the set of all Fourier transformable functions is defined and the proof that the Fourier transformable functions space is complete with our metric is given. The separability theorem and that the Fourier transformable functions space is disconnected are also discussed.

Keywords

Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 30 March 2024

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