Alexander A. Fedotov

fedotov
professor, Doctor of Sciences
email: fedotov.s@mail.ru a.fedotov@spbu.ru

 Directions of research

  • Asymptotic methods of mathematical physics (quasi-classical, short-wave and adiabatic asymptotics)
  • Spectral theory of ergodic Schr\»odinger operators
  • Analytic theory of difference equations on the complex plane

Basic Research papers

  1. Fedotov A. and Sandomirskiy F. An Exact Renormalization Formula for the Maryland Model. Communications in Mathematical Physics, 334(2): 1083-1099, 2015.
  2. Fedotov Alexander and Klopp Frederic. An exact renormalization formula for Gaussian exponential sums and applications. American Journal of Mathematics, 134(3):711-748, 2012.
  3. Fedotov A. and Klopp F. Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrodinger operators. Annales Scientifiques De L’Ecole Normale Superieure, 38(6):889-950, 2005.
  4. Fedotov A., Klopp F. Anderson transitions for a family of almost periodic Schrodinger equations in the adiabatic case. Communications in Mathematical Physics 227(1):1-92, 2002.
  5. Fedotov A. and Klopp F. A complex WKB method for adiabatic problems. Asymptotic Analysis, 27(3-4): 219-264, 2001.
  6. Buslaev V. and Fedotov A. On the difference equations with periodic coefficients. Advances in Theoretical and Mathematical Physics 5(6):1-45, 2001.
  7. Buslaev, V. and Fedotov A. The Harper equation: monodromization without quasiclassics. St. Petersburg Math. J. 8(2):231-254, 1997.
  8. Buslaev, V., and Fedotov, A.. The monodromization and Harper equation. Séminaire Équations aux dérivées partielles (dit «Goulaouic-Schwartz») 1993-1994: 1-21, http://eudml.org/doc/112086.
  9. Buslaev V. S., Fedotov, A. A. The complex WKB method for the Harper equation. St. Petersburg Math. J. 6(3): 495-517, 1995.
  10. Buslaev, V. S.; Fedotov, A. A. Influence jf a horizontal inhomogeneity layer on sound-propagation in a deep-sea under non-adiabatic conditions. Soviet Physics Acoustics, 32(1): 16-18, 1986.

See also reviews:

  1. Fedotov A. Monodromization method in the theory of almost-periodic equations. St Petersburg Mathematical Journal, 25(2):303-325, 2014.
  2. Fedotov A. Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator. Journal of Mathematical Sciences, 173(3): 320-339, 2011.
  3. Fedotov A. Adiabatic almost-periodic Schrödinger operators. Journal of Mathematical Sciences Volume: 173(3): 299-319, 2011.

Teaching

  1. Lectures «Calculus» for the 2st year students: integration in \({\mathbb R}^n\), differetial forms, differential equations, Fourier analysis, calculus of variations
  2. Facultative lectures «Introduction to the mathematical theory of chaos»
  3. Lectures «Spectral theory of periodic and ergodic operators» for Master students

Scientific supervisor of undergraduate, graduate and post-graduate students

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