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Browsing by Subject "integral operator"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Spectrum localization of a perturbed operator in a strip and applications
    (Wydawnictwa AGH, 2021) Gil', Michael
    Let $A$ and $\tilde{A}$ be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of $A$ lie in some strip. In what strip the spectrum of $\tilde{A}$ lies if $A$ and $\tilde{A}$ are »close«? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    μ-Hankel operators on Hilbert spaces
    (Wydawnictwa AGH, 2021) Mirotin, Adolf; Kuzmenkova, Ekaterina
    A class of operators is introduced ($\mu$-Hankel operators, $\mu$ is a complex parameter), which generalizes the class of Hankel operators. Criteria for boundedness, compactness, nuclearity, and finite dimensionality are obtained for operators of this class, and for the case $\mu=1$ their description in the Hardy space is given. Integral representations of $\mu$-Hankel operators on the unit disk and on the Semi-Axis are also considered.