Polynomial Harmonic Decompositions

Abstract

For real polynomials in two indeterminates a classical polynomial harmonic decomposition (cf. (1) below) is extended from square-norm divisors to conic ones. The main result is then applied to obtain a full polynomial harmonic decomposition, and to solve a Dirichlet problem with polynomial boundary data.

Keywords

• real polynomial
• harmonic function
• harmonic decomposition
• dirichlet problem
• primary 31a05
• secondary 31a25