Abstract:
We investigate the linear conjugation problem for polyanalytic functions using function theory and Caucliy-type integrals. We explicitly construct a canonical matrix-function by using the recurrence procedure and use it to study the linear conjugation problem. We found a solutions of the linear conjugation problem and given a formula for its index by using Cauchy type integrals. We got a representation of the solution of the linear conjugation problem through the canonical matrix-function, which is constructed explicitly.
Keywords:linear conjugation problems, the goursat formula, cauchy singular integral, functions of canonic matrices, singular integral equations.
