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113, Birkh¨ auser, Basel, 2000. [111] M. S. Shapiro, The Friedrichs operator of a planar domain II, Recent advances in operator theory and related topics (Szeged, 1999), 519–551, Oper. Theory Adv. Appl. 127, Birkh¨ auser, Basel, 2001. [112] S. Richardson, Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel, J. Fluid Mech. 56 (1972), 609–618. [113] S. Richardson, Hele-shaw flows with time-dependent free boundaries involving a multiply connected fluid region, European J.

295– 305 in “Potential Theory” (editors J. Kral, I. Netuka, J. Vesely), Plenum Publishing Corporation, 1988. [126] M. Sakai, An index theorem on singular points and cusps of quadrature doamins, Holomorphic functions and moduli, Vol. I (Berkeley, CA, 1986), 119–131, Math. Res. Inst. , 10, Springer, New York, 1988. [127] M. Sakai, Regularity of boundary having a Schwarz function, Acta Math. 166 (1991), 263–297. [128] M. Sakai, Regularity of free boundaries in two dimensions, Ann. Scuola Norm Sup.

1). However, even if Ω is a quadrature domain for subharmonic functions, so that it is uniquely determined by {(ak , ck )}, no general method is known for effectively determining the remaining polynomials Q0 , . . , Qn−2 from {(ak , ck )}. 1) for analytic h. For example, it can be used to prove analyticity of ∂Ω, see [52], thereby providing an alternative approach to [127], [128], [129]. For further results on hyponormal operators and quadrature domains, see [103], [105], [157], [161], [159], and for connections to moment problems also the survey [108].

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