Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations
Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations
In this paper we study multivariate polynomial functions in complex variables and their corresponding symmetric tensor representations. The focus is to find conditions under which such complex polynomials always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, characterize the conditions for such complex …