Free Martingale polynomials for stationary Jacobi processes

Abstract

We generalize a previous result concerning free martingale polynomials for the stationary free Jacobi process of parameters $\lambda \in ]0.1],\theta =1/2$. Hopelessly, apart from the case $\lambda =1$, the polynomials we derive are no longer orthogonal with respect to the spectral measure. As a matter of fact, we use the multiplicative renormalization to write down the corresponding orthogonality measure.

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