Related papers: Formal and convergent solutions of analytic equati…
In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result and a similar result of P{\l}oski, he conjectured that this…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the…
We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.
First we recall the notion of conxity and log-convexity for real-valued. Then we generalize the trick used by Artin in his famous paper on the Gamma function to find log-convex solutions to the functional equations f(x+1)=g(x)f(x). This…
We give a new and elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the…
We survey the classical results of the Dirichlet Approximation Theorem.
A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.
We study various approximation results of solutions of equations $f(x,Y)=0$ where $f(x,Y)\in\mathbb K[[x]][Y]^r$ and $x$ and $Y$ are two sets of variables, and where some components of the solutions $y(x)\in\mathbb K[[x]]^m$ do not depend…
Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to…
Using notions of homogeneity we give new proofs of M. Artin's algebraicity criteria for functors and groupoids. Our methods give a more general result, unifying Artin's two theorems and clarifying their differences.
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…