Biorthogonal wavelet on a logarithm curve \(\mathbb{C}\) (Q2034627)

Summary: 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.