Abstract
We consider a radiation solution \(\psi\) for the Helmholtz equation in an exterior domain in \(\mathbb{R}^2\) . We show that \(\psi\) in the exterior domain is uniquely determined by its imaginary part \(\operatorname{Im}(\psi)\) on an interval of a line \(L\) lying in the exterior domain. This result has a holographic prototype in the recent paper by Nair and Novikov (2025, J. Geom. Anal. 35, 4, 123). Some other curves for measurements, instead of the lines \(L\) , are also considered. Applications to the Gelfand–Krein–Levitan inverse problem (from boundary values of the spectral measure in \(\mathbb{R}^2\) ) and to passive imaging are also indicated.
DOI 10.1134/S1061920825601077
