Classifications and duality relations for several integral transforms

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.