In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Privacy preservation has become a major issue in many data analysis applications. When a data set is released to other parties for data analysis, privacy-preserving techniques are often required to reduce the possibility of identifying sensitive information about individuals. However, many solutions exist for privacy preserving data; differential privacy has emerged as a new paradigm for privac...

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general solutions of differential operators. In particular, the harmonic Bessel RBF transforms were presented for high-dimensional data processing. It was also found ...