Errata: “On the plane sections method for functions of two variables” (Quart Appl. Math. 30 (1972/73), 481–490)
Tabitha L. McCoy · Quarterly of Applied Mathematics · 1974
The last paragraph of the proof of Lemma 4.1 is not correct.We provide here a corrected proof of the assertion that if p(X:) = c° and the pn are free of zeros in some neighborhood of Xi , then p(X) = ® in a full neighborhood of \i .By hypothesis, lim^ log |p"(X,)| = -co, n->oo ân ordinary limit.Because the functions (1 /n) log |p"(X)| are harmonic and bounded above in a disc about X! , we can subtract off an appropriate constant and use Harnack's inequality ([1], p. 235) to infer the result.Indeed, it then follows from the subharmonic property of these functions that p = <» in the entire plane.We may as well mention that in the definition of r(X) in this paper, g.l.b. should be replaced by l.u.b.