Registration Number
0221U000218,
0120U105316
, R & D reports
Title
It is best to approximate polynomials with constraints and without constraints and a system of subspaces.
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Head
Shevchuk Ihor О., Доктор фізико-математичних наук
Registration Date
03-01-2021
Organization
Taras Shevchenko National University of Kyiv
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The object of research is systems of closed subspaces of Hilbert space, which have the property of inverse best approximation property (IBAP), systems of marginal subspaces. The aim of the work is to obtain different formulas (different from the formulas of PL Combettes and NN Reyes) for solving the problem of the inverse best approximation with the lowest norm, to establish the connection between the property of the inverse best approximation property (IBAP) and Riesz families, to prove that the systems of root subspaces of continuous linear operators possess IBAP, to prove that if the system of closed subspaces of Hilbert space possesses IBAP, then it is a system of eigen subspaces of some continuous operator. Obtain a sufficient condition for a system of marginal subspaces generated by discrete random variables from a certain class to have IBAP. Obtain the necessary condition for a system of marginal subspaces generated by discrete random variables from a certain class to have IBAP. Research methods - methods of functional analysis and operator theory.
Product Description
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Motorna Oksana V.
Petrova Iryna L.
Feshchenko Ivan S.
Shteglov Mykyta V.
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2021-01-03
