We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A=A+\alpha\left\langle\cdot,\omega_1\right\rangle\omega_2$, $\omega_1\not=\omega_2$, $\alpha\in{\mathbb C}$, in a general case $\omega_1,\omega_2\in{\mathcal H}_{-2}$. Using a constructive description of the perturbed operator $\tilde A$, we investigate some spectral and approximations properties of $\tilde A$. The wave operators corresponding to the couple $A$, $\tilde A$ and a series of examples are also presented.
Mykola Dudkin and Tetiana Vdovenko, On nonsymmetric rank one singular perturbations of selfadjoint operators, Methods Funct. Anal. Topology 22
(2016), no. 2, 137-151.
BibTex
@article {MFAT841,
AUTHOR = {Dudkin, Mykola and Vdovenko, Tetiana},
TITLE = {On nonsymmetric rank one singular perturbations of selfadjoint operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {2},
PAGES = {137-151},
ISSN = {1029-3531},
MRNUMBER = {MR3522856},
ZBLNUMBER = {06665384},
URL = {http://mfat.imath.kiev.ua/article/?id=841},
}
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