On the Uniform Stability of Recovering Sine-Type Functions with Asymptotically Separated Zeros

Abstract

We obtain the uniform stability of recovering entire functions of special form from their zeros. To such a form, we can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second orders, including differential systems with asymptotically separated eigenvalues whose characteristic numbers lie on a line containing the origin, as well as the nonlocal perturbations of these operators. We prove that the dependence of such functions on the sequences of their zeros is Lipschitz continuous with respect to natural metrics on each ball of a finite radius. Results of this type can be used for studying the uniform stability of inverse spectral problems. In addition, general theorems on the asymptotics of zeros of functions of this class and on their equivalent representation via an infinite product are obtained, which give the corresponding results for many specific operators.