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Multiple Orthogonal Polynomials of two real variables

Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Padé approximation, random matrix theory or integrable systems. However, this theory has only been studied in the univariate case. We give a generalization of Multiple Orthogonal Polynomials for two variables. Moreover, an extended version of some of the main properties are given. Additionally, some examples are given along the paper.