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Browsing by Subject "Riesz basis"

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  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Bazy w przestrzeniach Banacha
    (Data obrony: 2013-09-25) Szlęk, Magdalena
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Elementy teorii baz w przestrzeni Hilberta
    (Data obrony: 2018-03-15) Fornal, Natalia
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    The basis property of eigenfunctions in the problem of a nonhomogeneous damped string
    (2017) Rzepnicki, Łukasz
    The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator $iA$. We prove that the set of root vectors of the operator $A$ forms a basis of subspaces in a certain Hilbert space $H$. Furthermore, we give the rate of convergence for the decomposition with respect to this basis. In the second main result we show that with additional assumptions the set of root vectors of the operator $A$ is a Riesz basis for $H$.