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Displaying 921 –
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This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...
This paper deals with feedback stabilization of second order equations of
the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[,
where A0 is a densely defined positive selfadjoint linear operator on a
real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is
proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and
Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the
strong stabilization. This result is derived from a general compactness
theorem...
An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras...
We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP) are also presented.
In dimension one it is proved that the solution to a total variation-regularized
least-squares problem is always a function which is "constant almost everywhere" ,
provided that the data are in a certain sense outside the range of the operator
to be inverted. A similar, but weaker result is derived in dimension two.
Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak...
We prove the periodicity of all H2-local minimizers with low energy
for a one-dimensional higher order variational problem.
The results extend and complement an earlier work of Stefan Müller
which concerns the structure of global minimizer.
The energy functional studied in this work is motivated by the
investigation of coherent solid phase transformations and the
competition between the
effects from regularization and formation of small scale structures.
With a special choice of a bilinear double...
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