On the generalized Hartley and Hartley-Hilbert transformations

Advances in Difference Equations

Shrideh Khalaf Qasem Al-Omari¹  Adem Klman² 

[1] Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan;Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), Serdang, Malaysia

关键词: distributions;    test function;    HH transform;    Boehmians;   

DOI  :  10.1186/1687-1847-2013-222

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we extend Hartley and Hartley-Hilbert transformations (HT and HHT, respectively) to a certain space of tempered distributions. We then establish a certain convolution theorem for the HHT. The convolution theorem, obtained in this way, has been shown to possess a factorization property of Fourier convolution type. Proving the new convolution theorem for the HHT, by the usual convolution product, the transform is investigated on a certain space of Boehmians. Its properties of linearity and convergence are also discussed in the context of Boehmian spaces. MSC:54C40, 14E20, 46E25, 20C20.

【 授权许可】

CC BY