其他名称：
25-21-00118
项目负责人：
Akopyan Roman
发表日期：
2025
主持机构：
N.N.Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences,
国家：
俄罗斯
开始日期：
2025
结束日期：
2026
简介：
The project aims to study several topical problems in the theory of functions and operators. The best approximation and optimal recovery of the values of unbounded operators, primarily differentiation operators, on classes of smooth and holomorphic functions of one and several variables using incomplete and/or approximate information about the functions, such as approximately given values of functions on a mesh, and values of analytic functions on a subset of the boundary. Exact inequalities of the Kolmogorov type for differentiable and holomorphic functions.
The project includes the following studies.
1. The best pointwise differentiation of a function on the axis with respect to its approximate values on a fixed mesh for the class of functions with bounded higher derivative, and the related Kolmogorov-type inequality.
2. Optimal recovery of the values of differential operators on classes of analytic (holomorphic) functions of several complex variables from imprecisely given values on a subset of the Shilov boundary of the domain of analyticity; interrelated problems of best approximation of operators and exact inequalities.
3. Best approximation and optimal recovery of the differentiation operator on asymmetric classes of functions on the axis determined by the sign-sensitive norm of the higher derivative.
4. Optimal interpolation and extrapolation of the value of the derivative of a polynomial approximately defined on a compact set of the complex plane.
The scientific problems stated in the project are an important and difficult classical area of mathematics. It is of great importance both for the internal development of the theory and for applying in various branches of mathematics and its applications. In particular, when constructing optimal (best in accuracy) or close to optimal numerical methods.
A special feature of the project is its focus on studying several specific interconnected, complex, previously unstudied extreme problems, each of which can serve as a serious impetus for further development of the topic.
专业领域：
信息技术
语种：
英语
