Geodesic
Interpolation polynomials in Hilbert space and some extremum problems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 237-247.

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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. 
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     author = {V. V. Khlobystov},
     title = {Interpolation polynomials in {Hilbert} space and some extremum problems},
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V. V. Khlobystov. Interpolation polynomials in Hilbert space and some extremum problems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 237-247. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a18/