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Functional Analysis and Its Applications

, Volume 47, Issue 2, pp 157–159 | Cite as

Spaces of smooth functions generated by nonhomogeneous differential expressions

  • S. V. Kislyakov
  • D. V. Maksimov
  • D. M. Stolyarov
Article

Abstract

A Sobolev-type embedding theorem is established, which differs from classical statements in that the assumptions are imposed on linear combinations of the form \(\sum {a_j D^{a_j f_j } } \) with different functions f j and different multi-indices α j . It is applied to a classification problem for spaces of smooth functions generated by finite collections of differential expressions.

Key words

space of smooth functions isomorphism Sobolev embedding. 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. V. Kislyakov
    • 1
  • D. V. Maksimov
    • 2
  • D. M. Stolyarov
    • 3
  1. 1.St. Petersburg Department of the V. A. Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.P. L. Chebyshev research laboratory SPbGUSt. PetersburgRussia

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