On a Schauder basis related to the eigenvectors of a family of non-selfadjoint analytic operators and applications View Full Text


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Article Info

DATE

2013-12

AUTHORS

Ines Feki, Aref Jeribi, Ridha Sfaxi

ABSTRACT

In the present paper, we deal with the perturbed operator T(ε):=T0+εT1+ε2T2+⋯+εkTk+⋯,where ε∈C,T0 is a closed densely defined linear operator on a separable Banach space X with domain D(T0), while T1,T2,... are linear operators on X with the same domain D⊃D(T0) and satisfying a specific growing inequality. The basic idea here is to investigate under sufficient conditions assuring the invariance of the closure of the perturbed operator T(ε) which enables us to study the changed spectrum. Moreover, we prove that the system formed by some eigenvectors of T(ε) which are analytic on ε, forms a Schauder basis in X. After that, we apply the obtained results to a nonself-adjoint problem describing the radiation of a vibrating structure in a light fluid and to a nonself-adjoint Gribov operator in Bargmann space. More... »

PAGES

311-331

References to SciGraph publications

  • 1937-12. Störungstheorie der Spektralzerlegung in MATHEMATISCHE ANNALEN
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    http://scigraph.springernature.com/pub.10.1007/s13324-013-0060-y

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    http://dx.doi.org/10.1007/s13324-013-0060-y

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