Compact Hankel forms on planar domains
This paper is devoted to unify some basic questions in the theory of meromorphic approximation in the planar open set \(G\) which supports the Borel measure \(\mu\). To this end the authors start from the abstract theory of bilinear symmetric Hankel form defined on a complex separable Hilbert space \([.,.]\) satisfying \([fx,y]=[x,fy]\). The singular numbers (defined in Adamyan-Arov-Krein theorem) associated to Hankel operators with Markov functions as symbols, doubly orthogonal systems of analytic functions and Hadamard type determinants are investigated. The transition from Hardy space to the Bergman space associated to \(G\) is considered as well as the spectral theory of the Friedrichs operator of the domain \(G\) which leads to some qualitative features of the measure \(\mu\). A precise historical introduction related to the classical approximation theory questions concerned in this paper preceeds the abstract framework.
scientific article; zbMATH DE number 5604857