Results & Lemmas (4)
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LEMMA 1.
LEMMA 1. C* is a closed, convex set. Received June 24, 1957. The work reported on here was done while the writer held a National Science…
LEMMA 1. C* is a closed, convex set. Received June 24, 1957. The work reported on here was done while the writer held a National Science Foundation post doctoral Fellowship. The writer wishes to thank Pro- fessor M. Schiffer for many helpful conversations during the course of this work. 1381
LEMMA 2.
LEMMA 2. For I <^k <ίm, the polynomial Rk(z) is of the form with Here, each Ajtk and each Bhk is a polynomial in the αv and their…
LEMMA 2. For I <^k <ίm, the polynomial Rk(z) is of the form with Here, each Ajtk and each Bhk is a polynomial in the αv and their conjugates {independent of the λj, and the A Uk and BUJc satisfy the recursion relations
LEMMA 3.
LEMMA 3. For eachj,k, 0 <±j <Ln — k — 1, l<I&<^m, the AJtk and BJtl& of Lemma 2 satisfy the following: (i ) Auic is a polynomial in a2,…
LEMMA 3. For eachj,k, 0 <±j <Ln — k — 1, l<I&<^m, the AJtk and BJtl& of Lemma 2 satisfy the following: (i ) Auic is a polynomial in a2, α3, , aj+lύ and at, af, , α*_1# (ii) Bjtk is a polynomial in a2, α3, , aj+!ύ-1 and af, αf, , α*. (iii) Bι>k is real for any choice of α2, α3,
THEOREM 1.
THEOREM 1. Let (α2, α3,, an^) e F*-i. // (a.i9 α3,, an^) is an interior point of F * _ x then Ct aZJ •••, an-τ) is a circular disc…
THEOREM 1. Let (α2, α3, , an^) e F*-i. // (a.i9 α3, , an^) is an interior point of F * _ x then Ct{aZJ •••, an-τ) is a circular disc determined by \Ahn-.ι\=Bι>n_ι; furthermore