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Khan, Dawood, Emadifar, Homan, Ahmed, Ali, Iqbal, Saleem, Tariq, Muhammad. (1403). Some algebraic and topological structures of Fourier transformable functions. سامانه مدیریت نشریات علمی, 5(1), 70-79. doi: 10.22098/jfga.2024.14270.1109
Dawood Khan; Homan Emadifar; Ali Ahmed; Saleem Iqbal; Muhammad Tariq. "Some algebraic and topological structures of Fourier transformable functions". سامانه مدیریت نشریات علمی, 5, 1, 1403, 70-79. doi: 10.22098/jfga.2024.14270.1109
Khan, Dawood, Emadifar, Homan, Ahmed, Ali, Iqbal, Saleem, Tariq, Muhammad. (1403). 'Some algebraic and topological structures of Fourier transformable functions', سامانه مدیریت نشریات علمی, 5(1), pp. 70-79. doi: 10.22098/jfga.2024.14270.1109
Khan, Dawood, Emadifar, Homan, Ahmed, Ali, Iqbal, Saleem, Tariq, Muhammad. Some algebraic and topological structures of Fourier transformable functions. سامانه مدیریت نشریات علمی, 1403; 5(1): 70-79. doi: 10.22098/jfga.2024.14270.1109

Some algebraic and topological structures of Fourier transformable functions

Journal of Finsler Geometry and its Applications
دوره 5، شماره 1، 2024، صفحه 70-79    اصل مقاله (295.49 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
Fourier transform؛ Fourier transformable functions؛ Metric space؛ Connected space
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