Polyorthogonalization in Pre-Hilbert Spaces

For a set of measure and the corresponding scalar products, we define multiple analogues of the Gram determinants and matrices. With their help, we found criteria of uniqueness and explicit form of polyorthogonal functions, obtained as a result of the described process of polyorthogonalization of linearly independent systems in the pre-Hilbert function spaces generated by the measures . Our results generalize Schmidt’s theorem about orthogonalization.