| Abstract: |
| There is extensive mathematical and physical literature on the ill-posed inverse problem of deautoconvolution for the reconstruction of real-valued as well as complex-valued functions $x$ with support on the unit interval $[0,1] \subset \mathbb{R}$ from
its autoconvolution $y=x*x$, and we mention some application in laser optics.
However, little is known about the reconstruction of functions with support on the $d$-dimensional unit cube $[0,1]^d \subset \mathbb{R}^d$ from autoconvolution data. This talk presents recent analytical and numerical results for deautoconvolution in two and more dimensions with different types of data.
In particular, there are new assertions on uniqueness or twofoldness of solutions to the deautoconvolution problem in the multidimensional case, which are based on extensions of the Titchmarsh convolution theorem published by Lions and Mikusi\`{n}ski. |
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