ACTA issues

Simultaneous rational approximants to Nikishin Systems. II

Kathy Driver, Herbert Stahl

Acta Sci. Math. (Szeged) 61:1-4(1995), 261-284

Abstract. We continue the investigation of simultaneous rational approximants $(Q_1/Q_0,\ldots,Q_m/Q_0)$, with common denominator polynomial $Q_0$, to a vector of functions $(f_1,\ldots,f_m)$ that forms a Nikishin system. Rather complete results regarding the nature of the $m$th remainder function $R_m$ and the location of its zeros for a large class of normal multi--indices have been proved in [DrSt4]. In this paper, we shall analyse the zeros of the other $(m-1)$ remainder functions $R_1,\ldots,R_{m-1}$ for a class of multi--indices that is close to diagonal. To that end, we introduce auxiliary Nikishin systems which allow us to permute the order of the functions in the original system.

AMS Subject Classification (1991): 41A21, 30E10

Keyword(s): Nikishin systems, simultaneous rational approximants, normality, orthogonal polynomials, multiple orthogonality

Received February 20, 1995. (Registered under 5685/2009.)