Browsing by Subject "Fock space"

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Access status: Open Access ,
Matrices related to some Fock space operators
(2011) Rudol, Krzysztof
Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
Access status: Open Access ,
On the eigenvalues of a 2×2 block operator matrix
(2015) Muminov, Muhiddin Èškobilovič; Rasulov, Tulkin Husenovič
A $2×2$ block operator matrix ${\mathbf H}$ acting in the direct sum of one- and two-particle subspaces of a Fock space is considered. The existence of infinitely many negative eigenvalues of $H_{22}$ (the second diagonal entry of ${\mathbf H}$) is proved for the case where both of the associated Friedrichs models have a zero energy resonance. For the number $N(z)$ of eigenvalues of $H_{22}$ lying below z<0, the following asymptotics is found $\lim\limits_{z\to -0} N(z) |\log|z||^{-1}=\,{\mathcal U}_0 \quad (0\lt {\mathcal U}_0\lt \infty).$ Under some natural conditions the infiniteness of the number of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of ${\mathbf H}$ is proved.
Access status: Restricted ,
Przestrzeń Focka oraz operatorowa linearyzacja układów dynamicznych fizyki matematycznej
(Data obrony: 2017-06-12) Wodka, Natalia
Wydział Matematyki Stosowanej