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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 2, Pages 28–37 (Mi faa188)  

This article is cited in 6 scientific papers (total in 6 papers)

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

G. A. Kalyabinab

a 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
$$ K_0:=\frac4\pi\int_0^{\pi/4}\ln(\operatorname{\cot}x) dx=1.166243\ldots=\ln3.209912…. $$

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

DOI: https://doi.org/10.4213/faa188

Full text: PDF file (156 kB)
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English version:
Functional Analysis and Its Applications, 2002, 36:2, 106–113

Bibliographic databases:

UDC: 517.518.237, 512.643.5
Received: 19.10.2001

Citation: G. A. Kalyabin, “The Best Extension Operators for Sobolev Spaces on the Half-Line”, Funktsional. Anal. i Prilozhen., 36:2 (2002), 28–37; Funct. Anal. Appl., 36:2 (2002), 106–113

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. A. Kalyabin, “Extrapolations with the Least Norms in the Sobolev Spaces $W_2^n$ on the Half-Axis and the Whole Axis”, Proc. Steklov Inst. Math., 243 (2003), 220–226  mathnet  mathscinet  zmath
    2. Kalyabin G.A., “Best constants in Kolmogorov inequalities for the Sobolev space $W_2^n(\mathbb R_+)$”, Dokl. Math., 67:1 (2003), 24–26  mathnet  mathscinet  zmath  isi
    3. G. A. Kalyabin, “Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)”, Funct. Anal. Appl., 38:3 (2004), 184–191  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. G. A. Kalyabin, “Effective Formulas for Constants in the Stechkin–Gabushin Problem”, Proc. Steklov Inst. Math., 248 (2005), 118–124  mathnet  mathscinet  zmath
    5. G. A. Kalyabin, “Some Problems for Sobolev Spaces on the Half-line”, Proc. Steklov Inst. Math., 255 (2006), 150–158  mathnet  crossref  mathscinet  elib
    6. A. A. Lunev, L. L. Oridoroga, “Exact Constants in Generalized Inequalities for Intermediate Derivatives”, Math. Notes, 85:5 (2009), 703–711  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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