On the basis property for the root vectors of some nonselfadjoint operators

Ramm, Alexander G.

doi:10.1016/0022-247x(81)90091-3

Cited by 4 publications

(3 citation statements)

References 8 publications

(9 reference statements)

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“…In the both cases, we require precise knowledge of the spectrum of the corresponding non self-adjoint operators, more precisely, the behavior of the high frequency set. The advantage of our approach is that it works in any dimension and in a very general setting (see [15] and also [12]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Rate of decay of some abstract Petrowsky-like dissipative semi-groups

2015

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In this paper, we show that the fastest decay rate for some Petrowsky-like dissipative systems is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the corresponding operator satisfied some spectral gap condition. We give also some applications to illustrate our setting.2010 Mathematics Subject Classification. 74K10 (35Q72 35B40 34L20).

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Rate of decay of some abstract Petrowsky-like dissipative semi-groups

2015

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“…The following basic result can be concluded from the proof of a more general result in [14] (see also [15], [16, section V.4] …”

Section: Resultsmentioning

confidence: 99%

Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients

Guo¹

2002

SIAM J. Control Optim.

107

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Abstract. This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler-Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition, and the exponential stability are concluded. The results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam.

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“…A summary of main results of this theory is given in[20],[21],[3],[38]. On the basis property without brackets see[43].M. S. Agranovich [3] applied the theory of pseudo-differential operators to the integral equations of diffraction theory.S e c t i o n 3.…”

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confidence: 99%