Abstract: | We consider the Sturm-Liouville operator on a convex smooth curve lying in the complex plane and connecting the points 0 and 1. We prove that if the eigenvalues λk with large numbers are localized near a single ray, then this ray is the positive real semiaxis. Moreover, if the eigenvalues λk are numbered with algebraic multiplicities taken into account, then λk ∼ π · k as k → +∞.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 72–84.Original Russian Text Copyright © 2005 by Kh. K. Ishkin. |