Kashpur O.F.
Hermite–Birkhoff interpolation polynomial of minimum norm in Hilbert space

The Hermite–Birkhoff interpolation problem for a nonlinear operator in the Hilbert space is considered. For this problem, the theorem on the interpolation polynomial of minimum norm generated by a scalar product with a Gaussian measure is proved. Such interpolant is shown to be unique. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Gateaux differential, Hermite–Birkhoff interpolation polynomial, Hilbert space, minimum norm, Hilbert spaces, Interpolation, Mathematical operators, Polynomials, Gateaux differential, Gaussian measures, Hermite-Birkhoff interpolations, Hermite–birkhoff interpolation polynomial, Interpolants, Interpolation polynomials, Interpolation problems, Minimum norm, Nonlinear operator, Scalar product, Vector spaces

Cite:
Kashpur O.F. (2021). Hermite–Birkhoff interpolation polynomial of minimum norm in Hilbert space. Cybernetics and Systems Analysis, 57 (5), 150–155. doi: https://doi.org/10.1007/s10559-021-00405-2 http://jnas.nbuv.gov.ua/article/UJRN-0001268756 [In Ukrainian].