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Some algebraic and topological structures of Fourier transformable functions | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 5، شماره 1، مرداد 2024، صفحه 70-79 اصل مقاله (244.36 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2024.14270.1109 | ||
| نویسندگان | ||
| Dawood Khan1؛ Homan Emadifar* 2؛ Ali Ahmed1؛ Saleem Iqbal1؛ Muhammad Tariq3 | ||
| 1Department of Mathematics, University of Balochistan, Quetta, 87300, Pakistan | ||
| 2Department of Mathematics, Hamedan Branch, Islamic Azad University,Hamedan, Iran | ||
| 3Department of Baic Sciences, Mehran University of Engineering and Technology, Jamshoro, Pakistan | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Abelian group؛ Commutative semi-group؛ Disconnected space؛ Fourier transform؛ Separability theorem | ||
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آمار تعداد مشاهده مقاله: 84 تعداد دریافت فایل اصل مقاله: 73 |
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