Spectral shift function and eigenvalues of the perturbed operator
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 15-26
Voir la notice de l'article provenant de la source Math-Net.Ru
In the space of square-integrable functions on the positive semi-axis, two positive selfadjoint operators are constructed that are generated by a one-dimensional free Hamiltonian. These operators are employed to construct a pair of spectrally absolutely continuous bounded selfadjoint operators whose difference is an operator of rank $1$. Then the perturbation determinant is used to find an explicit form of the M. G. Krein spectral shift function for this pair. It is shown that despite the $A$-smoothness of the perturbation in the sense of Hölder, the point $\lambda = 1$, where the spectral shift function has a discontinuity of the first kind, is not an eigenvalue of the perturbed operator.
@article{ZNSL_2022_512_a1,
author = {A. R. Aliev and E. H. Eyvazov},
title = {Spectral shift function and eigenvalues of the perturbed operator},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {15--26},
publisher = {mathdoc},
volume = {512},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a1/}
}
A. R. Aliev; E. H. Eyvazov. Spectral shift function and eigenvalues of the perturbed operator. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 15-26. http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a1/