Orthogonal polynomials on the unit circle and their derivatives (Q810804)

A well-known result by W. Hahn says that the only orthogonal polynomials on the real line for which the derivatives are also orthogonal on the real line are the classical orthogonal polynomials named after Jacobi, Laguerre and Hermite. The present paper gives a characterization along the same line for orthogonal polynomials on the unit circle: it is shown that the only family of orthogonal polynomials on the unit circle for which also the derivatives are orthogonal on the unit circle are the polynomials \(\phi_ n(z)=z^ n\) which are orthogonal with respect to Lebesgue measure on the unit circle.