An application of doubly orthogonal functions to a problem of approximation in two regions
Philip J. Davis · Transactions of the American Mathematical Society · 1952
1. Introduction. In the plane of the complex variable z, let there be given two regions G and B which are bounded and such that GCB. The regions may be simply- or multiply-connected, but will be considered to satisfy certain additional conditions which will be formulated precisely in a subsequent paragraph. We shall designate by L2(G) the set of functions which are singlevalued and regular in G and which possess a finite norm: