Results & Lemmas (4)
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THEOREM 1.
THEOREM 1. The solution to the extremal problem max l(f) is given by (3) provided that the residue a belongs to the disk A of values…
THEOREM 1. The solution to the extremal problem max l(f) is given by (3) provided that the residue a belongs to the disk A of values determined by the inequality \a\p (4) 5-> (1 + p)6 \a + p \ 2
THEOREM 2.
THEOREM 2. Let g(z) be an extremal function for the problem max Iff) and assume that extigfU) ^ <j>. Then ' -1 <g,Q o g> = Um r+1 -1 r Qfw)…
THEOREM 2. Let g(z) be an extremal function for the problem max Iff) and assume that extigfU)} ^ <j>. Then ' -1 <g,Q o g> = Um r+1 -1 r Qfw) dw\ = 0
COROLLARY 2.1.
COROLLARY 2.1. Suppose that <x °° g(Z) = + I a,3, z - p 0 k k is an extremal function for the problem max A (f) and that ext g(U) ? <f>. If…
COROLLARY 2.1. Suppose that <x °° g(Z) = + I a,3, z - p 0 k k is an extremal function for the problem max A (f) and that ext{g(U)} ? <f> . If we set and then ag(z) <»
COROLLARY 2.2.
COROLLARY 2.2. Suppose that g(z) = z - p 0 K is an extremal function for the problem max A(f) feS (a) P and that extlg(U) =? <!>. Then…
COROLLARY 2.2. Suppose that g(z) = z - p 0 K is an extremal function for the problem max A(f) feS (a) P and that extlg(U)} =? <!> . Then either afe = 0 for all k > 2 or for infinitely many k > 2 .
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