BIORTHOGONAL SYSTEMS OF RATIONAL FUNCTIONS AND BEST APPROXIMATION OF THE CAUCHY KERNEL ON THE REAL AXIS

This paper is devoted to problems of the representation and best approximation of the Cauchy kernel on the whole real axis - ∞ < x < + ∞. The method proposed here for the solution of such problems is based on the attraction of systems of rational functions with fixed poles which are orthogonal or biorthogonal on the whole axis. Bibliography: 9 items.