Increasing stability in the inverse source problem with many frequencies

We study increasing stability in the interior inverse source problem for the Helmholtz equation from boundary Cauchy data for multiple wave numbers. By using the Fourier transform with respect to the wave number, explicit bounds for the analytic continuation, uniqueness of the continuation results, and exact observability bounds for the wave equation, a sharp uniqueness result and an increasing (with larger wave numbers intervals) stability estimate are obtained. Numerical examples in 3 spatial dimension support the theoretical prediction.