Abstract. In this paper we give an overview of the discretization results connected to Malmquist--Takenaka systems for the unit disc and upper half-plane. We prove that the discretization nodes on the real line have similar properties like the discretization nodes on the unit circle: for example they satisfy some equilibrium conditions and they are stationary points of some logarithmic potential. The problems whether they are the minimum of a logarithmic potential is formulated and solved in a special case.

DOI: 10.14232/actasm-015-765-6

AMS Subject Classification (1991): 42C05, 33C50, 33A65, 41A20, 30H10, 42B30, 65T99

Keyword(s): Hardy spaces, Malmquist--Takenaka systems, discrete orthogonality, equilibrium conditions

Received February 17, 2015, and in revised form March 18, 2015. (Registered under 15/2015.)