NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (1), P. 63–78
ON SOME APPLICATIONS OF THE BOUNDARY CONTROL METHOD TO SPECTRAL ESTIMATION AND INVERSE PROBLEMS
S. A. Avdonin – Department of Mathematics and Statistics, University of Alaska, Fairbanks, USA; s.avdonin@alaska.edu
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, St. Petersburg, Russia; mikhaylov@pdmi.ras.ru
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, St. Petersburg, Russia; vsmikhaylov@pdmi.ras.ru
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, Schrödinger equation, hyperbolic system.
PACS 02.30 Zz, 02.30 Yy, 02.30 Nw
DOI 10.17586/2220-8054-2015-6-1-63-78