Biorthogonal Wavelet on a Logarithm Curve ℂ

Abstract

According to the length-preserving projection and Euler discretization method, biorthogonal wavelet function on a smooth curve $\mathcal{C}$ is constructed in this paper, such as a logarithm curve. The properties of biorthogonal wavelet filters on a smooth curve $\mathcal{C}$ are discussed, such as induced refinable equation and symmetry. Moreover, an example is given for discussing the biorthogonal scaling function and its dual on a logarithm curve $\mathcal{C}$ . Finally, a numerical application is given for dealing with financial data.