In 1996, Ricardo Ricardo Mañé discovered that Mather measures are in fact the minimizers of a ”universal” infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Mañé obtained the first estimation of that sort by using finite dimensional approximations. Recently, we we...

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case. Namely, convex functions are always considered to be defined on convex sets with nonempty interior. But typically, ...

Various researchers have studied examples of innnite-dimensional dynamical systems. In most of the cases, the phase space consisted of a Hilbert or Banach space or a Frechet space of functions. In this article we propose to study a dynamical system, namely the geodesic ow, over more structurally complex manifolds, the tangent bundles of a family of Hilbert Grassmannians. Using the high degree o...

The minimum backward Fréchet distance (MBFD) problem is a natural optimization problem for the weak Fréchet distance, a variant of the well-known Fréchet distance. In this problem, a threshold ε and two polygonal curves, T1 and T2, are given. The objective is to find a pair of walks on T1 and T2, which minimizes the union of the portions of backward movements while the distance between the movi...

This paper presents cone compression and expansion fixed point results of KrasnoselskiiPetryshyn type formultimaps between Fréchet spaces. Two approaches have recently been presented in the literature, both of which are based on the fact that a Fréchet space can be viewed as a projective limit of a sequence of Banach spaces {En}n∈N (here N= {1,2, . . .}). Both approaches are based on constructi...

For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number ρ0 such that for α > ρ0 the problem under consideration is uniquely solvable in the Frechet space. In the case where the coefficients are constants, Bochner’s method is developed in multidimensional domains, and used to prove the uniquely so...

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

Abstract The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on simplex system of equations gas dynamics in the mixed Euler-Lagrangian variables. To find solution such scheme at time step, it represented as single equation nonlinear function two arguments from space – direct product spaces gas-dynamic quantities. ...

Last decade, at rst the variational problems in Sobolev spaces, later the Radon-Nikodym problem in vector integration, and some other problems leads us to the new function characteristics, both scalar and convex compact, which are closely connected to a certain decomposition of the space under consideration. That decomposition is generated by the Banach subspaces spanned by the all absolutely c...