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Browsing by Subject "creation operator"

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    Item type:Article, Access status: Open Access ,
    A note on inductive limit model of Bargmann space of infinite order
    (2005) Stochel, Jerzy
    It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction $a=(a_1,a_2,\ldots) \in l^2$ are inductive limits of the creation and annihilation operator acting on Bargmann space of $n$-th order.
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    Item type:Article, Access status: Open Access ,
    A remark on generalized commutation relation and subnormality
    (2006) Stochel, Jerzy Bartłomiej
    Tillmann [Tillmann H. G., <i>Zur Eindeutigkeit der Losungen der quanten mechanischen vertauschungrelationen</i>, Acta Sci. Math. (Szeged) 24 (1963), 258-270] proved that every operator $A$ which fulfils the canonical commutation relation $A^{*}A - AA^{*} = Id$ is an orthogonal sum of canonical creation operators. We extend this result for operators which fulfil generalized commutation relations $A^{*}A - AA^{*}= E^2,\text{ where }EA = AE.$ In addition, some inequalities which are helpful in describing analytic vectors of operators $A^{*}A$, where $A$ fulfils the generalized commutation relation, are established.
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Przestrzeń Focka oraz operatorowa linearyzacja układów dynamicznych fizyki matematycznej
    (Data obrony: 2017-06-12) Wodka, Natalia
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Przesunięcia ważone na grafach
    (Data obrony: 2015-07-13) Kiełtyka, Ewa
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Subnormalność uogólnionych operatorów kreacji
    (Data obrony: 2015-07-13) Kończyk, Łukasz
    Wydział Matematyki Stosowanej