Abstract
We construct and study orthogonal bases of generalized polynomials on the space of Hermitian matrices. They are obtained by the Gram–Schmidt orthogonalization process from the Schur polynomials. A Berezin–Karpelevich type formula is given for these multivariate polynomials. The normalization of the orthogonal polynomials of Hermitian matrix argument and expansions in such polynomials are investigated.
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