Goldberg’s constants
نویسنده
چکیده
0 < A0 = A1 = A3 < A2 = A4 < 0.0319, and extremal functions for A0 and A2 exist, but extremal functions for A1, A3 and A4 they do not exist. This is a simple normal families argument; it also shows that extremal functions for A0 have the boundary of the ring {z : A0 < |z| < 1} as the natural boundary, and extremal functions for A2 have the unit circle as the natural boundary. The problem is to find the constants A0 and A2 and extremal functions. Theorem 1.
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