Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A2 (G\K) and A2(G) be the Bergman spaces on G\K, respectively G and define N = A2(G\K) Ɵ A2 (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator Cf = PNTf│N, where f ϵ C(G) and Tf is the Toeplitz operator on A2(G\K).
Copyright © 1991 Indiana University Mathematics Journal. This article first appeared in Indiana University Mathematics Journal 40:4 (1991), 1363-1386.
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Ross, William T. "Analytic Continuation in Bergman Spaces and the Compression of Certain Toeplitz Operators." Indiana University Mathematics Journal 40, no. 4 (1991): 1363-1386.