A parametric representation for k-variable Schur polynomials

A parametric representation for k-variable polynomials with prescribed partial degrees is given, where the coefficients are functions of real parameter vectors. For these parameters, simple conditions which are sufficient to guarantee that the corresponding polynomials are widest-sense Schur are established. Simple necessary and sufficient conditions are introduced in the two-variable case so that the corresponding polynomials are scattering Schur. The synthesis of two-dimensional lossless one-ports and a parametric representation of constant unitary matrices form the basis of these considerations