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排序方式: 共有49条查询结果,搜索用时 15 毫秒
1.
Let{T (t)}t≥0 be a C0-semigroup on an infinite-dimensional separable Hilbert space; a suitable definition of near{T (t)~*}t≥0 invariance of a subspace is presented in this paper. A series of prototypical examples for minimal nearly{S(t)~*}t≥0 invariant subspaces for the shift semigroup{S(t)}t≥0 on L2(0,∞) are demonstrated, which have close links with near T~*_θ invariance on Hardy spaces of the unit disk for an inner function θ. Especially, ... 相似文献
2.
The admissibility of observation operators and control operators for linear Volterra systems is studied by means of the theory of composition operators on Hardy spaces.Under certain assumptions it is shown to be equivalent to admissibility for the classical Cauchy problem. A duality between control and observation operators is also established,extending known results for the Cauchy problem,which is a special case. 相似文献
3.
This paper shows that the boundedness of a weighted composition operator on the Hardy–Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators. 相似文献
4.
For a contraction operator T with spectral radius less than one on a Banach space
, it is shown that the factorization of certain L1 functions by vectors x in
and x*. in
, in the sense that
for n ≧ 0, implies the existence of invariant subspaces for T. Explicit formulae for such factorizations are given in the case of weighted composition operators on reproducing kernel
Hilbert spaces. An interpolation result of McPhail is applied to show how this can be used to construct invariant subspaces
of hyperbolic weighted composition operators on H2.
Received: 1 November 2005 相似文献
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Zohra Bendouad Isabelle Chalendar Jean Esterle Jonathan R. Partington 《数学学报(英文版)》2010,26(12):2239-2254
This paper is concerned first with the behaviour of differences T(t) - T(s) near the origin, where (T(t)) is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane (in which case it is assumed analytic). For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T(t) -T(2t) have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator. 相似文献
8.
We study invariant subspaces in the context of the work of Katavolos and Power [9] and [10] when one of the semigroups considered
is replaced by a discrete one. As a consequence, a rather striking connection is given with the study of the lattice of invariant
subspaces of composition operators induced by automorphisms of the unit disc acting on the classical Hardy space. As a particular
instance, our study concerns the lattice of invariant subspaces of those composition operators induced by hyperbolic automorphisms,
and therefore with the Invariant Subspace Problem.
Partially supported by Plan Nacional I+D grant no. MTM2006-06431 and Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64. 相似文献
9.
Birgit Jacob Jonathan R. Partington Sandra Pott 《Complex Analysis and Operator Theory》2009,3(3):697-727
In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic
functions in weighted Hp spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of
p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces. 相似文献
10.
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The methods used in the analysis are based on the theory of reverse Carleson embeddings. 相似文献