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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.


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Article Information

TitleOn extensions of linear functionals with applications to non-symmetrically singular perturbations
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 193-206
MilestonesReceived 03/06/2018; Revised 24/06/2018
CopyrightThe 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


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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},
       URL = {http://mfat.imath.kiev.ua/article/?id=1082},
}


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