Control theory of distributed parameter systems
Nonharmonic Fourier series
Inverse problems of mathematical physics
Signal processing (sampling and interpolation of band-limited and multi-band signals, spectral estimation)
Partial differential and differential-difference equations
Control and inverse problems for differential equations on graphs
Main publications:
Avdonin, S.; Lenhart, S.; Protopopescu, V., “Solving the dynamical inverse problem for the Schrödinger equation by the boundary control method”, Inverse Problems, 18:2 (2002), 349–361
Avdonin, S.; Mikhaylov, V.; Rybkin, A., Communications in Mathematical Physics, 275:3 (2007), 791–803
Maxwell, D.; Truffer, M.; Avdonin, S.; Stuefer, M., “An iterative scheme for determining glacier velocities and stresses”, Journal of Glaciology, 54:188 (2008), 888–898
Avdonin, S.; Leugering, G.; Mikhaylov, V., “On an inverse problem for tree-like networks of elastic strings”, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 90:2 (2010), 136–150
