Polynomial solutions to certain higher-order non-Hermitian difference equations satisfy J-orthogonality (or left J-orthogonality) with respect to a positive matrix measure on the circle.
Zagorodnyuk, Direct and inverse spectral problems for (2N+1)- diagonal, complex, symmetric, non-Hermitian matrices, Serdica Math
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On the orthogonality of solutions for higher-order non-Hermitian difference equations
Polynomial solutions to certain higher-order non-Hermitian difference equations satisfy J-orthogonality (or left J-orthogonality) with respect to a positive matrix measure on the circle.