Hilbert boundary value problems of polyanalytic functions on the unit circumference

摘要

In this article, the Hilbert boundary value problem (BVP) for bianalytic functions with different factors on the unit circumference is first investigated in two different ways. The different expressions of the solutions and the conditions of solvability are obtained and the corresponding equivalence among them is verified. Then, the general Hilbert BVP for polyanalytic functions is studied by transforming it into the equivalent Hilbert BVP for a system of analytic functions, and the expressions of the solution and the solvability condition dependent on the so-called canonical matrix is obtained.