Normalized Gompertz wavelets and their application

Abstract

In the present paper, we define the Gompertz wavelets and show their basic properties. In particular, we prove that the admissibility condition holds for them. We also compute the normalizing factors in the space of square intergrable functions $L^{2}(\mathbb{R})$ and present an explicit formula for them in terms of the Bernoulli numbers. Then, after implementing the second-order Gompertz wavelets into Matlab's Wavelet Toolbox, we apply them to study the spread of the Covid-19 pandemic in Saudi Arabia.