Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014
Attorney at CBS Corporation, San Francisco CA, United States
The modern study of inverse problems and imaging applies a wide range of geometric and analytic methods which in turn creates new connections to various fields of mathematics, ranging from geometry, microlocal analysis and control theory to mathematical physics, stochastics and numerical analysis. Research in inverse problems has shown that many results of pure mathematics are in fact crucial components of practical algorithms. For example,a theoretical understanding of the structures that ideal measurements should reveal, or of the non-uniqueness of solutions,can lead to a dramatic increase in the quality of imaging applications. On the other hand,inverse problems have also raised many new mathematical problems. For example, the invention of the inverse spectral method to solve the Korteweg-de Vries equation gave rise to the field of integrable systems and the mathematical theory of solitons.
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Urszula Ledzewicz, Heinz Schättler. Pitfalls in applying optimal control to dynamical systems: An overview and editorial perspective. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022016
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