Registration Number
0222U000770,
0121U111197
, R & D reports
Title
Best approximation by polynomials with constraints and without constraints and subsystem systems
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Head
Shevchuk Ihor O., Доктор фізико-математичних наук
Registration Date
18-01-2022
Organization
Taras Shevchenko National University of Kyiv
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The object of the research is the form-preserving approximation of periodic functions, estimates of the best approximation by polynomials with Hermitian interpolation, systems of closed subspaces of Hilbert and Banach spaces.
Objective - To build a theory of co-convex approximation of periodic functions by trigonometric polynomials. Prove the falsity of classical estimates in the form-preserving approximation of q-convex functions, q> 2. Strengthen and / or generalize known estimates of point approximation of functions by algebraic polynomials, prove their ordinal accuracy, apply the apparatus of separated differences by Jacob's weight. Obtain formulas for solving the problem of inverse best approximation with the lowest norm, establish the relationship between the property of inverse best approximation property (IWAR) and Riesz families, prove that systems of root subspaces of fixed height of continuous linear operators have IWAR . Obtain sufficient and necessary conditions for the system of marginal subspaces generated by discrete random variables of a certain class to have IVAR. Identify and investigate the numerical characteristics of IVAR. Investigate the question of the closure and maximum sum of the subspaces of the space of operators (operating from one Banach space to another), which consist of operators whose cores contain the given subspaces.
Research methods - methods of function theory, functional analysis and operator theory.
Product Description
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Voloshyna Viktoriia O
Motorna Oksana V.
Petrova Iryna L.
Feshchenko Ivan S.
Shteglov Mykyta V.
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2022-03-09
