Analytic Continuation in Bergman Spaces and the Compression of Certain Toeplitz Operators
نویسندگان
چکیده
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) e 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 8G that do not intersect K. This result will be used to discuss the Fredholm theory of the operator a, = PNTJIN, where I E C(G) and T1 is the Toeplitz operator on A2(G\K).
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