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For the inverse source problem with the two-dimensional Helmholtz equation,the singular values of the 'source-to-near field' forward operator reveal asharp frequency cut-off in the stably recoverable information on the source. Weprove and numerically validate an explicit, tight lower bound for the spectrallocation of this cut-off. We also conjecture and support numerically a tightupper bound for the cut-off. The bounds are expressed in terms of zeros ofBessel functions of the first and second kind.

Explicit tight bounds on the stably recoverable information for the inverse source problem