Malmquist-Takenaka systems and equilibrium conditions (Q2770653)

The Malmquist-Takenaka system (\(\phi^a_n\), \(n\in N^*\)) form an orthonormal system on the unit circle \(T\). The restriction of the finite (\(\phi^a_n\), \(n=1,\dots,N\)) to a subset \(T^a_N\) of \(T\) is a discrete orthonormal system with respect to the scalar product \([ \cdot , \cdot ]\). It is shown that the set \(T^a_N\) can be interpreted as a solution of an electrostatic equilibrium problem. The zeros of Jacobi, Laquerre and Hermite polynomials admit a similar interpretation.