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.
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},
}