On some applications of the boundary control method to spectral estimation and inverse problems
https://doi.org/10.17586/222080542015616378
Abstract
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for these problems and show that the solvability of these equations crucially depends on the controllability properties of the corresponding dynamical system and properties of the corresponding families of exponentials.
Keywords
spectral estimation problem,
boundary control method,
identification problem,
inverse problem,
Schr¨odinger equation,
hyperbolic system
Supporting agencies: Sergei Avdonin was supported by the NSF grant DMS 1411564; Alexander Mikhaylov was supported by NSh1771.2014.1, RFBR 140100306, IRSES (FP7PEOPLE2012IRSES Marie Curie Actions); Victor Mikhaylov was supported by RFBR 140100535, RFBR 140131388 and NIR SPbGU 11.38.263.2014.
About the Authors
S. A. Avdonin
Department of Mathematics and Statistics, University of Alaska
United States
United States
Fairbanks
A. S. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State University, Faculty of Mathematics and Mechanics
Russian Federation
Russian Federation
St. Petersburg
V. S. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy
of Sciences; St. Petersburg State University, Faculty of Physics
Russian Federation
Russian Federation
St. Petersburg
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Review
For citations:
Avdonin S.A., Mikhaylov A.S., Mikhaylov V.S. On some applications of the boundary control method to spectral estimation and inverse problems. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(1):63–78. https://doi.org/10.17586/222080542015616378
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