Continuous Generalized Hankel-type integral wavelet transformation

Abstract

Using the theory of Hankel-type convolution, continuous generalized Hankel-type  wavelet integral transformation is defined. The generalized Hankel-type integral wavelet transformation is developed.  Using the developed theory of generalized Hankel-type convolution, the generalized Hankel-type translation is introduced. Properties of the kernel  are developed in the study. Using the properties of kernel,D _{μ,α, Î² ,v} (x,y,z)the generalized Hankel-type wavelet transformation is defined. The existence of the generalized Hankel-type integral wavelet transformation is given by a theorem. The boundedness and inversion formula for the generalized Hankel-type integral wavelet transformation is obtained. A basic wavelet which defines continuous generalized Hankel-type integral wavelet transformation, its admissibility conditions and the wavelet to the function is proved. Examples have been shown to explain the studied continuous generalized Hankel-type integral wavelet transformation.