15 citations · 24 across the 8 of their papers we have counts for
8 papers
A Tropical Version of the Schauder Fixed Point Theorem
G. B. Shpiz, G. L. Litvinov
A tropical version of the Schauder fixed point theorem for compact subsets of tropical linear spaces is proved.
Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach
G. L. Litvinov, G. B. Shpiz
In the framework of idempotent mathematics, analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of nuclear spaces (in the s…
Nuclear semimodules and kernel theorems in idempotent analysis. An algebraic approach
Grigori Litvinov, Grigori Shpiz
In this note we describe conditions under which, in idempotent functional analysis, linear operators have integral representations in terms of idempotent integral of V. P. Maslov.…
Idempotent (Asymptotic) Mathematics and the Representation Theory
Grigori Litvinov, Viktor Maslov, Grigori Shpiz
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathemati…
A theorem on eigenvectors in idempotent spaces
Grigori Shpiz
This paper suggests an algebraic version of the theorem on the existence of eigenvectors for linear operators in abstract idempotent spaces. Earlier, the theorem on the existence o…
Tensor products of idempotent semimodules. An algebraic approach
Grigori Litvinov, Viktor Maslov, Grigori Shpiz
We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are simulated on the algebraic level. This is one of a se…