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Mat. Zametki, 2025 Volume 117, Issue 3, Pages 333–343 (Mi mzm14548)

Uniform stability of the Hochstadt–Lieberman problem

N. P. Bondarenkoabcd

a Saratov State University
b Samara National Research University
c Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
d Moscow Center for Fundamental and Applied Mathematics

Abstract: The paper proves the uniform stability of the Hochstadt–Lieberman problem which consists in recovering the potential of the Sturm–Liouville operator on half the interval from the spectrum and the known potential on the other half of the interval. The proof method is based on the uniform stability of the direct and inverse Sturm–Liouville problems, of recovering a sine-type function from its zeros, and on the uniform boundedness of Riesz bases of sines and cosines.

Keywords: inverse spectral problem, half-inverse problem, uniform stability.

UDC: 517.984

MSC: 34A55 34B05 34B09 34L40

Received: 16.10.2024

DOI: 10.4213/mzm14548


 English version:
Mathematical Notes, 2025, 117:3, 357–365


© Steklov Math. Inst. of RAS, 2025