# Alexander A. 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.

1. Lectures «Calculus» for the 2st year students: integration in $${\mathbb R}^n$$, differetial forms, differential equations, Fourier analysis, calculus of variations