Approximation Theorems for the Group G2

Approximation theorems for group valued functions

Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuous functions C(X,G) (X compact, G a topological group) to be uniformly dense. These criteria are based on the existence of so-called condensing functions, where a continuous function φ : G → G is said to be condensing ...

Inverse Approximation Theorems for . . .

The Classical Artin Approximation Theorems

The various Artin approximation theorems assert the existence of power series solutions of a certain quality Q : formal, analytic, algebraic, of systems of equations of the same quality Q, assuming the existence of power series solutions of a weaker quality Q’ < Q : approximated, formal. The results are frequently used in commutative algebra and algebraic geometry. We present a systematic argum...

Ergodic Theorems and Approximation Theorems with Rates

A-ergodic nets and A-regularized approximation processes of operators are introduced and their convergence theorems are discussed. There are strong convergence theorems, uniform convergence theorems, theorems on optimal convergence, and theorems on non-optimal convergence and its sharpness. The general results provide unified approaches to investigation of convergence rates of ergodic limits an...

Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of thema...