Functional analysis, idempotent and tropical mathematics, representations of Lie groups, hypergroups, rational approximations, interval analysis, numerical methods, computer technologies.
Main publications:
G. L. Litvinov, “Representation of groups in locally convex spaces and topological group algebras”, Selecta Math. Sovietica, 7:2 (1988), 101–182
G. L. Litvinov, “Hypergroups and hypergroup algebras”, Journal of Soviet Math., 38 (1987), 1734–1761
G. L. Litvinov, “Approximation properties of locally convex spaces
and the problem of uniqueness of the trace of a linear operator”, Selecta Math. Sov., 11:1 (1992), 25–40
G. L. Litvinov, “Error autocorrection in rational approximations and interval estimates”, E-print journal, Central European Journal of Mathematics, 1:1 (2003), 36–60
G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, Journal of Mathematical Sciences, 140:3 (2007), 426–444
