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Sobolev-Slobodetskii spaces

  • Vladimir B. Vasil’ev
Chapter

Abstract

Let s be an arbitrary real number. By definition the Sobolev-Slobodetskii space H s (ℝ m ) consists of distributions u for which their Fourier transforms are locally integrable functions ũ(ξ)such that
$$ \left\| u \right\|_s^2 = {\int\limits_{{\mathbb{R}^m}} {\left| {\mu \left( \xi \right)} \right|} ^2}{\left( {1 + \left| \xi \right|} \right)^{2s}}d\xi < + \infty .$$
(3.1.1)

Keywords

Compact Support Integrable Function Differentiable Function Convex Cone Restriction Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Vladimir B. Vasil’ev
    • 1
  1. 1.Department of Mathematical AnalysisNovgorod State UniversityNovgorodRussia

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