On the basis property of root vectors related to a non-self-adjoint analytic operator and applications

• Autorzy: Ellouz Hanen , Feki Ines , Jeribi Aref

Identyfikatory

DOI

10.7862/rf.2022.3

• Języki publikacji: EN

Abstrakty

EN

In the present paper, based on a separation condition on the spectrum of a self-adjoint operator T0 on a separable Hilbert space H, we prove that the system of root vectors of the perturbed operator T (ε) given by T (ε) := T0 + εT1 + ε2T2 + . . . + εkTk + . . . is complete and forms a basis with parentheses in H, for small enough |ε|. Here ε ∈ C and T1, T2, . . . are linear operators on H having the same domain D ⊃ D(T0) and satisfying a specific growing inequality. The obtained results are of importance for applications to a non-self-adjoint Gribov operator in Bargmann space and to a non-self-adjoint problem deduced from a perturbation method for sound radiation.

Słowa kluczowe

EN

basis with parentheses; elastic membrane; Gribov operator; not condense; spectrum

PL

membrana elastyczna; operator Gribova; widmo

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2022
• Tom: Vol. 45
• Strony: 59--86
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Ellouz Hanen

• Département de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisie

• https://orcid.org/0000-0003-3801-7898

autor

Feki Ines

• Département de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisie

• https://orcid.org/0000-0003-0046-8298

autor

Jeribi Aref

• Département de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisie

• https://orcid.org/0000-0001-6715-5996

Bibliografia

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