Let Ω be a domain in the plane whose boundary is composed of a finite number of disjoint smooth simple closed curves. The space H~2(Ω) consists of those analytic functions f on Ω for which the subharmonic function | f(z) |~2 has a harmonic majorant. K(Ω) is the convex cone of those elements in H~2(Ω) whose real part is nonnegative on Ω. In this paper we describe the projection of H~2(Ω) onto K (Ω) and also describe the unique element of K(Ω) of minimal norm satisfying a finite number of interpolation conditions: min{ ||f||_(H~2(Ω)) : f ∈ K(Ω) and f(z_j) = w_j, j = 1,2,...,n}, (1.1) assuming, of course, that there is at least one element of K(Ω) satisfying these conditions.
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