40 citations · 52 across the 8 of their papers we have counts for
9 papers
Dequantization of Mathematics, idempotent semirings and fuzzy sets
G. L. Litvinov
In this talk a brief survey of basic ideas of Idempotent Mathematics is presented. Relations between this theory and the theory of fuzzy sets as well as the possibility theory and…
Idempotent/tropical analysis, the Hamilton-Jacobi and Bellman equations
Grigory L. Litvinov
Tropical and idempotent analysis with their relations to the Hamilton-Jacobi and matrix Bellman equations are discussed. Some dequantization procedures are important in tropical an…
Hypergroups and Hypergroup Algebras
Grigory L. Litvinov
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of h…
Approximation Properties of Locally Convex Spaces and the Problem of Uniqueness of the Trace of a Linear Operator
Grigory L. Litvinov
In the present article, it is proved that every nuclear operator in a locally convex space E has a well-defined trace if E possesses the approximation property. However, even if a…
Integral geometry, hypergroups, and I.M. Gelfand's question
M. I. Graev, G. L. Litvinov
This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are…
Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry
Grigory L. Litvinov
A brief introduction to tropical and idempotent mathematics (with an emphasys on idempotent functional analysis) is presented. Applications to classical mechanics and geometry are…