Education

1981 — Ph.D. (C.Sc.) in Mathematics and Physics («Differential Equations and Mathematical Physics»)
Institution: Leningrad State University
Advisor: M.Z. Solomyak

Scientific interests

Spectral theory of differential operators, asymptotic methods.

Selected publications

1. A. Karol', A. Nazarov and Ya. Nikitin (2008). Small ball probabilities for Gaussian random fields and tensor products of compact operators. Transactions of the American Mathematical Society 360(3), 1443–1474.
2. A.I. Karol' (2009). Newton polyhedra, asymptotics of volumes, and asymptotics of exponential integrals. American Mathematical Society Translations (Series 2) 228, 13–30.
3. A.I. Karol' and A.I. Nazarov (2014). Small ball probabilities for smooth Gaussian fields and tensor products of compact operators. Mathematische Nachrichten 287(5–6), 595–609.
4. A.I. Karol (2017). Asymptotics of spectra of compact pseudodifferential operators with nonsmooth symbols with respect to spatial variables. Journal of Mathematical Sciences 226(4), 355–374.