One-dimensional quaternion Mellin transforms and its applications. (English) Zbl 1500.44005
Summary: In this study, one-dimensional quaternion Mellin transform with properties like linearity, scaling, shifting, differentiation and convolution type property are demonstrated. The Parseval-type property and inversion theorem are also established. To support the study, applications from mathematical physics are given in the concluding section.
MSC:
44A35 | Convolution as an integral transform |
44A05 | General integral transforms |
46S05 | Quaternionic functional analysis |