This article is cited in 6 papers

The Best Extension Operators for Sobolev Spaces on the Half-Line

G. A. Kalyabin<sup>ab

a</sup> S. P. Korolyov Samara State Aerospace University
^b Samara Academy of Humanities

Abstract: We describe the construction of extension operators with minimal possible norm $\tau_m$ from the half-line to the entire real line for the spaces $W_2^m$ and derive the asymptotic estimate $\ln\tau_m\approx K_0m$ (as $m\to\infty$), where
$$ K_0:=\frac4\pi\int_0^{\pi/4}\ln(\operatorname{\cot}x)\,dx=1.166243\ldots=\ln3.209912\dots. $$

The proof is based on the investigation of the maximum and minimum eigenvalues and the corresponding eigenvectors of some special matrices related to Vandermonde matrices and their inverses, which can be of interest in themselves.

Keywords: extrapolations with minimal norms, Vandermonde matrices.

UDC: 517.518.237, 512.643.5

Received: 19.10.2001

DOI: 10.4213/faa188

 English version: Functional Analysis and Its Applications, 2002, 36:2, 106–113

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