Classifications and duality relations for several integral transforms
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Authors
Xin Liang
- State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Feng Gao
- State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Shan-Jie Su
- State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Zhen Wang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Xiao-Jun Yang
- State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Abstract
In this paper, we classify several integral transforms into two
categories according to the types of their kernel functions and two novel
definitions of general integral transforms are suggested. Based on the general integral transforms, some of their
basic properties are proved. In addition, the dualities between those
two kinds of integral transforms are deducted and discussed in detail. The interesting
coupling relations in symmetric form is illustrated graphically. The
analysis shows that the classifications are reasonable and the dualities are
significant.
Share and Cite
ISRP Style
Xin Liang, Feng Gao, Shan-Jie Su, Zhen Wang, Xiao-Jun Yang, Classifications and duality relations for several integral transforms, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6324--6332
AMA Style
Liang Xin, Gao Feng, Su Shan-Jie, Wang Zhen, Yang Xiao-Jun, Classifications and duality relations for several integral transforms. J. Nonlinear Sci. Appl. (2017); 10(12):6324--6332
Chicago/Turabian Style
Liang, Xin, Gao, Feng, Su, Shan-Jie, Wang, Zhen, Yang, Xiao-Jun. "Classifications and duality relations for several integral transforms." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6324--6332
Keywords
- Integral transforms
- kernel functions
- dualities
MSC
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