Uniform Stability of the Hochstadt–Lieberman Problem

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.