On extensions of linear functionals with applications to non-symmetrically singular perturbations

Abstract

The article is devoted to extensions of linear functionals, generated by scalar products, in a scale of Hilbert spaces. Such extensions are used to consider non-symmetrically singular rank one perturbations of ${\mathcal H}_{-2}$-class. For comparison, we give main definitions and descriptions of singular non-symmetric perturbations of ${\mathcal H}_{-1}$ and ${\mathcal H}_{-2}$-classes.

Key words: Scale of Hilbert spaces, functional, rigged Hilbert spaces, singular perturbations.

Full Text

Article Information

Title	On extensions of linear functionals with applications to non-symmetrically singular perturbations
Source	Methods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 193-206
MathSciNet	MR3860802
Milestones	Received 03/06/2018; Revised 24/06/2018
Copyright	The Author(s) 2018 (CC BY-SA)

Authors Information

M. Dudkin
National Technical University of Ukraine (KPI), 37 Peremogy Av., Kyiv, 03056, Ukraine

T. Vdovenko
National Technical University of Ukraine (KPI), 37 Peremogy Av., Kyiv, 03056, Ukraine

Citation Example

Mykola Dudkin and Tetiana Vdovenko, On extensions of linear functionals with applications to non-symmetrically singular perturbations, Methods Funct. Anal. Topology 24 (2018), no. 3, 193-206.

BibTex

@article {MFAT1082,
    AUTHOR = {Mykola Dudkin and Tetiana Vdovenko},
     TITLE = {On extensions of linear functionals with applications to non-symmetrically singular perturbations},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {193-206},
      ISSN = {1029-3531},
  MRNUMBER = {MR3860802},
       URL = {http://mfat.imath.kiev.ua/article/?id=1082},
}

References

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