ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 41, 15 Kalyabin, Gennadiy A. Samara State Aerospace University, Russia On extentions from “one-point set” with minimal norms in Bernstein and Sobolev classes Let U_{m}(β, θ), β, θ > 0 and Φ_{m} stand (resp.) for the matrices inverse to the Hilbert matrix H_{m}(β, θ) := ∥ β^{j+k}(j + k + θ)^{−1}∥, 0 ≤ j, k ≤ m and to the Vandermonde matrix V (λ_{1}, …, λ_{m}) where {λ_{s}} is the set of all roots of the degree 2m of (−1)^{m+1} situated in the left halfplane. Basing on new sharp estimates for maximal elements of U_{m}(β, θ) and Φ_{m} the asymptotic behavior of the least possible norms of extrapolations is established for the case when the number of initial conditions tends to infinity. Reference: Maz’ya, V. L. Sobolev spaces. - Springer Verlag, Berlin, 1985.