共查询到20条相似文献,搜索用时 11 毫秒
1.
Bernhard H. Haak Peer Christian Kunstmann 《Integral Equations and Operator Theory》2006,55(4):497-533
We study linear systems, described by operators A, B, C for which the state space X is a Banach space.We suppose that − A generates a bounded analytic semigroup and give conditions for admissibility of B and C corresponding to those in G. Weiss’ conjecture. The crucial assumptions on A are boundedness of an H∞-calculus or suitable square function estimates, allowing to use techniques recently developed by N. Kalton and L. Weis. For observation spaces Y or control spaces U that are not Hilbert spaces we are led to a notion of admissibility extending previous considerations by C. Le Merdy. We also obtain a characterisation of wellposedness for the full system. We give several examples for admissible operators
including point observation and point control. At the end we study a heat equation in X = Lp(Ω), 1 < p < ∞, with boundary observation and control and prove its wellposedness for several function spaces Y and U on the boundary ∂Ω. 相似文献
2.
The Weiss conjecture on admissibility of observation operators for contraction semigroups 总被引:4,自引:0,他引:4
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that
for alls in the open right half-plane. HereA denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators. 相似文献
3.
4.
We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on
for
or
and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in
or
相似文献
5.
Zen Harper 《Integral Equations and Operator Theory》2006,54(1):69-88
In this paper, we study a discrete version of the Weiss Conjecture. In Section 1 we discuss the Reproducing Kernel Thesis
and in Section 2 we introduce the operators which concern us. Section 3 shows how to relate these operators to Carleson embeddings
and weighted composition operators, so that we can apply the Carleson measure theorem to obtain conditions for boundedness
and compactness of many weighted composition operators. Section 4 contains Theorem 4.4 which is a discrete version of the
Weiss Conjecture for contraction semigroups, and finally Section 5 shows how the usual (continuous time) Weiss Conjecture
is related to the discrete version studied here; in fact they are equivalent (for scalar valued observation operators). The
main advantage of the discrete version is that it is technically simpler – the observation operators are automatically bounded
and the functional calculus can be achieved using power series. 相似文献
6.
Benoit Florent Sehba 《Integral Equations and Operator Theory》2008,62(2):233-245
We present here some criteria for Schatten-Von Neumann class membership for the small Hankel operator on Bergman space A
2(T
Ω), when T
Ω is the tube over the symmetric cone Ω.
The author would like to thank professor Aline Bonami for helpful advices. 相似文献
7.
We define Toeplitz operators on all Dirichlet spaces on the unit ball of
and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive
symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman
spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting
case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of
bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate
some connections between Toeplitz and shift operators.
The research of the second author is partially supported by a Fulbright grant. 相似文献
8.
Ovidiu Furdui 《Integral Equations and Operator Theory》2008,60(4):469-483
In this paper we consider the space where dv
s
is the Gaussian probability measure. We give necessary and sufficient conditions for the boundedness of some classes of integral
operators on these spaces. These operators are generalizations of the classical Bergman projection operator induced by kernel
function of Fock spaces over .
相似文献
9.
We study four transformations which lead from one well-posed linear
system to another: time-inversion, flow^-inversion, time-flow-inversion and
duality. Time-inversion means reversing the direction of time, flow-inversion
means interchanging inputs with outputs, while time-flow-inversion means doing
both of the inversions mentioned before. A well-posed linear system is
time-invertible if and only if its operator semigroup extends to a group. The
system is flow-invertible if and only if its input-output map has a bounded
inverse on some (hence, on every) finite time interval [0, ] ( > 0). This is
true if and only if the transfer function of has a uniformly bounded inverse
on some right half-plane. The system is time-flow-invertible if and only if
on some (hence, on every) finite time interval [0, ], the combined operator
from the initial state and the input function to the final state and the output
function is invertible. This is the case, for example, if the system is conservative,
since then is unitary. Time-flow-inversion can sometimes, but not
always, be reduced to a combination of time- and flow-inversion. We derive a
surprising necessary and sufficient condition for to be time-flow-invertible:
its system operator must have a uniformly bounded inverse on some left halfplane.
Finally, the duality transformation is always possible.We show by some
examples that none of these transformations preserves regularity in general.
However, the duality transformation does preserve weak regularity. For all
the transformed systems mentioned above, we give formulas for their system
operators, transfer functions and, in the regular case and under additional
assumptions, for their generating operators. 相似文献
10.
In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform
is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence
of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6]. 相似文献
11.
Catalin Badea 《Advances in Mathematics》2007,211(2):766-793
We study increasing sequences of positive integers (nk)k?1 with the following property: every bounded linear operator T acting on a separable Banach (or Hilbert) space with supk?1‖Tnk‖<∞ has a countable set of unimodular eigenvalues. Whether this property holds or not depends on the distribution (modulo one) of sequences (nkα)k?1, α∈R, or on the growth of nk+1/nk. Counterexamples to some conjectures in linear dynamics are given. For instance, a Hilbert space operator which is frequently hypercyclic, chaotic, but not topologically mixing is constructed. The situation of C0-semigroups is also discussed. 相似文献
12.
In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize classes of perturbations preserving the strong stability of the semigroup. In addition, we improve recent results on preservation of polynomial stability of a semigroup under perturbations of its generator. Theoretic results are illustrated with an example where we consider the preservation of the strong stability of a multiplication semigroup. 相似文献
13.
14.
Complementing and generalizing classical as well as recent results, we prove asymptotically optimal formulas for the Gelfand
and approximation numbers of identities En ↪ Fn, where En and Fn denote the n-th sections of symmetric quasi-Banach
sequence spaces E and F satisfying certain interpolation assumptions. We illustrate our
results by considering classical spaces such as Lorentz and Orlicz sequence spaces.
Supported by DFG grant Hi 584/2-2. 相似文献
15.
James E. Jamison 《Integral Equations and Operator Theory》2006,56(4):469-482
A pair of operators on a Banach space X are isometrically equivalent if they are intertwined by a surjective isometry of X. We investigate the isometric equivalence problem for pairs of operators on specific types of Banach spaces. We study weighted
shifts on symmetric sequence spaces, elementary operators acting on an ideal I of Hilbert space operators, and composition operators on the Bloch space. This last case requires an extension of known results
about surjective isometries of the Bloch space. 相似文献
16.
In this paper we consider a class of weighted integral operators onL
2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided. 相似文献
17.
Wolfgang Arendt 《Positivity》2008,12(1):25-44
Extending results of Davies and of Keicher on ℓp we show that the peripheral point spectrum of the generator of a positive bounded C0-semigroup of kernel operators on Lp is reduced to 0. It is shown that this implies convergence to an equilibrium if the semigroup is also irreducible and the
fixed space non-trivial. The results are applied to elliptic operators.
Dedicated to the memory of H.H. Schaefer 相似文献
18.
19.
Yoichi Uetake 《Integral Equations and Operator Theory》2005,51(2):283-302
We prove some local properties of the spectrum of a linear dynamical system in Hilbert space. The semigroup generator, the control operator and the observation operator may be unbounded. We consider (i) the PBH test, (ii) the correspondence between the poles of the resolvent of the semigroup generator and the poles of the transfer function, and (iii) pole-zero cancellation between two transfer functions of the cascade connection of two dynamical systems. For our investigation we take well-posed linear systems and a subclass of them called weakly regular systems as the most general setting. 相似文献
20.
Olivia Constantin 《Integral Equations and Operator Theory》2007,59(4):523-554
We prove a general atomic decomposition theorem for weighted vector-valued Bergman spaces, which applies to duality problems
and to the study of compact Toeplitz type operators.
相似文献