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Ukrainian Mathematical Journal

, Volume 60, Issue 5, pp 810–815 | Cite as

On the defect of nondenseness of continuous imbeddings in the scale of Hilbert spaces

  • R. V. Bozhok
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We obtain a formula for the determination of a defect under a continuous imbedding of subspaces in the scale of Hilbert spaces.

Keywords

Hilbert Space Singular Perturbation Proper Subset Separable Hilbert Space Orthogonal Subspace 
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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References

  1. 1.
    Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators, American Mathematical Society, Providence, RI (1968).Google Scholar
  2. 2.
    Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables, American Mathematical Society, Providence, RI (1986).Google Scholar
  3. 3.
    S. Albeverio, W. Karwowski, and V. Koshmanenko, “Square power of singularly perturbed operators,” Math. Nachr., 173, 5–24 (1995).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Albeverio, R. Bozhok, M. Dudkin, and V. Koshmanenko, “Dense subspace in scales of Hilbert spaces,” Meth. Funct. Anal. Top., 11, No. 2, 156–169 (2005).zbMATHMathSciNetGoogle Scholar
  5. 5.
    R. Bozhok and V. Koshmanenko, “Singular perturbations of self-adjoint operators associated with rigged Hilbert spaces,” Ukr. Mat. Zh., 57, No. 5, 622–632 (2005).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    V. Koshmanenko, “Construction of singular perturbations by the method of rigged Hilbert spaces,” J. Phys. A: Math. Gen., 38, 4999–5009 (2005).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • R. V. Bozhok
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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