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Ukrainian Mathematical Journal

, Volume 65, Issue 3, pp 435–447 | Cite as

Extended Sobolev Scale and Elliptic Operators

  • V. A. Mikhailets
  • A. A. Murach
Article

We obtain a constructive description of all Hilbert function spaces that are interpolation spaces with respect to a pair of Sobolev spaces \( \left[ {{H^{{\left( {{s_0}} \right)}}}\left( {{{\mathbb{R}}^n}} \right),{H^{{\left( {{s_1}} \right)}}}\left( {{{\mathbb{R}}^n}} \right)} \right] \) of some integer orders s 0 and s 1 and form an extended Sobolev scale. We propose equivalent definitions of these spaces with the use of uniformly elliptic pseudo-differential operators positive-definite in \( {L_2}\left( {{{\mathbb{R}}^n}} \right) \). Possible applications of the introduced scale of spaces are indicated.

Keywords

Hilbert Space Sobolev Space Elliptic Operator Pseudodifferential Operator Interpolation Space 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • V. A. Mikhailets
    • 1
  • A. A. Murach
    • 1
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKievUkraine

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