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.
This publication is cited in the following 11 articles:
N. P. Bondarenko, “Ravnomernaya ustoichivost zadachi Khokhshtadta–Libermana”, Matem. zametki, 117:3 (2025), 333–343
Feng Wang, Chuan-Fu Yang, Sergey Buterin, Nebojs̆a Djurić, “Inverse spectral problems for Dirac-type operators with global delay on a star graph”, Anal.Math.Phys., 14:2 (2024)
Feng Wang, Chuan-Fu Yang, “Inverse problems for Dirac operators with constant delay less than half of the interval”, Journal of Mathematical Physics, 65:3 (2024)
B. Vojvodić, V. Vladičić, N. Djurić, “Inverse problem for Dirac operators with two constant delays”, Journal of Inverse and Ill-posed Problems, 2023
M. Kuznetsova, “Uniform stability of recovering Sturm–Liouville-type operators with frozen argument”, Results Math., 78:5 (2023), 169
N. P. Bondarenko, “Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition”, Bol. Soc. Mat. Mex., 29:1 (2023), 2
S. Buterin, S. Vasilev, “An inverse Sturm–Liouville-type problem with constant delay and non-zero initial function”, Mathematics, 11:23 (2023), 4764
S. Buterin, “Functional-differential operators on geometrical graphs with global delay and inverse spectral problems”, Results Math., 78:3 (2023), 79
Nebojsa Djuric, Biljana Vojvodic, “Inverse problem for Dirac operators with a constant delay less than half the length of the interval”, Appl Anal Discrete Math, 17:1 (2023), 249
Sergey Buterin, “On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra”, Mathematics, 11:12 (2023), 2688
S. Buterin, N. Djurić, “Inverse problems for Dirac operators with constant delay: uniqueness, characterization, uniform stability”, Lobachevskii J. Math., 43:6 (2022), 1492