Complex Harmonic Splines, Periodic Quasi-Wavelets : Theory and Applications

This book presents Complex Harmonic Splines (CHS), which gives an approximation to the Complex Harmonic Function (CHF), in particular the conformal mapping with high accuracy from the unit disc to a domain with arbitrary shape. The volume develops various periodic quasi-wavelets which can be used to solve the Helmholtz integral equation under some boundary conditions with complexity O(N). The last part of the work introduces a class of periodic wavelets with various properties. Audience: This volume will be of interest to applied mathematicians, physicists and engineers whose work involves approximations and expansions, integral equations, functions of a complex variable and numerical analysis.