Interpolation polynomials in Hilbert space and some extremum problems

V. V. Khlobystov

National Taras Shevchenko University of Kyiv

Abstract: In abstract Hilbert space the whole set of the polynomial interpolants is constructed. In Hilbert space with measure the interpolation polynomial with minimum norm is found, the problem for the best approximation value of the linear continuous functional on a bounded convex set of the operator interpolants is solved. Interpretation of these results is considered for the multivariable functions.

UDC: 519.65+519.62.50

Received: 01.01.1998

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