共查询到20条相似文献,搜索用时 15 毫秒
1.
Adam Bobrowski 《Journal of Evolution Equations》2007,7(3):555-565
Let
be a locally compact Hausdorff space. Let A and B be two generators of Feller semigroups in
with related Feller processes {X
A
(t), t ≥ 0} and {X
B
(t), t ≥ 0} and let α and β be two non-negative continuous functions on
with α + β = 1. Assume that the closure C of C
0 = αA + βB with
generates a Feller semigroup {T
C
(t), t ≥ 0} in
. It is natural to think of a related Feller process {X
C
(t), t ≥ 0} as that evolving according to the following heuristic rules. Conditional on being at a point
, with probability α(p) the process behaves like {X
A
(t), t ≥ 0} and with probability β(p) it behaves like {X
B
(t), t ≥ 0}. We provide an approximation of {T
C
(t), t ≥ 0} via a sequence of semigroups acting in
that supports this interpretation. This work is motivated by the recent model of stochastic gene expression due to Lipniacki
et al. [17]. 相似文献
2.
Enrico Priola 《Journal of Evolution Equations》2006,6(4):577-600
We consider the diffusion semigroup Pt associated to a class of degenerate elliptic operators
. This class includes the hypoelliptic Ornstein-Uhlenbeck operator but does not satisfy in general the well-known H?rmander
condition on commutators for sums of squares of vector fields. We establish probabilistic formulae for the spatial derivatives
of Pt f up to the third order. We obtain L∞-estimates for the derivatives of Pt f and show the existence of a classical bounded solution for the parabolic Cauchy problem involving
and having
as initial datum.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
3.
Robert J. Taggart 《Mathematische Zeitschrift》2009,261(4):933-949
Suppose that {T
t
: t ≥ 0} is a symmetric diffusion semigroup on L
2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem
and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence. 相似文献
4.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
5.
We consider a generalization of the Stokes resolvent equation, where the constant viscosity is replaced by a general given
positive function. Such a system arises in many situations as linearized system, when the viscosity of an incompressible,
viscous fluid depends on some other quantities. We prove that an associated Stokes-like operator generates an analytic semi-group
and admits a bounded H
∞
-calculus, which implies the maximal L
q
-regularity of the corresponding parabolic evolution equation. The analysis is done for a large class of unbounded domains
with -boundary for some r > d with r ≥ q, q′. In particular, the existence of an L
q
-Helmholtz projection is assumed. 相似文献
6.
7.
Mustapha Mokhtar-Kharroubi 《Journal of Evolution Equations》2008,8(2):327-352
We deal with streaming operators T
H
defined in L
1 spaces by the directional derivative with positive boundary operator H of norm 1 relating the incoming and outgoing fluxes. It is known that T
H
need not be a generator but there exists a contraction semigroup generated by an extension A of T
H
. This paper deals with the total mass carried by individual trajectories {e
tA
f; t ≥ 0} for nonnegative initial data f and related topics. In particular, our analysis covers the problem of (the lack of) stochasticity of {e
tA
; t ≥ 0} for conservative boundary operator H.
相似文献
8.
Sebastian Król 《Journal of Evolution Equations》2009,9(3):449-468
The concept of the gap function is used to give new perturbation results for generators of holomorphic semigroups. In particular, we show that if A is the generator of a holomorphic semigroup on a Banach space and , then every closed linear operator C such that for some and
generates a holomorphic semigroup, too. Moreover, we obtain an analogue of this result for differences of semigroups. If T is a holomorphic semigroup and , then every C
0-semigroup S with
is holomorphic. We also give certain estimates for the constants M
A
and k
T
appearing in the above conditions.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr N201384834. 相似文献
9.
We give some new examples of bounded multilinear forms on the Hilbert spaces ℓ2 and L2 (0, ∞). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ≥ 3) on ℓ2 which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent
on
where
相似文献
10.
11.
We consider the Schr?dinger operator Hγ = ( − Δ)l + γ V(x)· acting in the space
where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
We study the asymptotic behavior as
of the non-bottom negative eigenvalues of Hγ, which are born at the moment γ = 0 from the lower bound λ = 0 of the spectrum σ(H0) of the unperturbed operator H0 = ( − Δ)l (virtual eigenvalues). To this end we use the Puiseux-Newton diagram for a power expansion of eigenvalues of some class of
polynomial matrix functions. For the groups of virtual eigenvalues, having the same rate of decay, we obtain asymptotic estimates
of Lieb-Thirring type. 相似文献
12.
In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence
where Ad = (I + A) (I − A)−1.
We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, then power boundedness of Ad is equivalent to the uniform boundedness of the semigroup generated by A. 相似文献
13.
Pascale Vitse 《Archiv der Mathematik》2005,85(4):374-385
For Banach space operators T satisfying the Tadmor-Ritt condition
a band limited H∞ calculus is established,
where
and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus,
These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived.
Received: 25 October 2004; revised: 31 January 2005 相似文献
14.
Summary. Let k ≥ 1 be any integer. Let G be a finite abelian group of exponent n. Let sk(G) be the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum subsequence of length kn. We study this constant for groups
when d = 3 or 4. In particular, we prove, as a main result, that
for every k ≥ 4,
and
for every prime p ≥ 5. 相似文献
15.
Roberto Stasi 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):419-436
In this paper we are interested in studying the properties of an elliptic degenerate operator N0 in the space Lp of
with respect to an invariant measure μ. The existence of μ is proven under suitable conditions on coefficients of the operator.
We prove that the closure of N0 is m-dissipative in
相似文献
16.
Peer Christian Kunstmann 《Archiv der Mathematik》2008,91(2):178-186
We consider the Stokes operator A on unbounded domains of uniform C
1,1-type. Recently, it has been shown by Farwig, Kozono and Sohr that – A generates an analytic semigroup in the spaces , 1 < q < ∞, where for q ≥ 2 and for q ∈ (1, 2). Moreover, it was shown that A has maximal L
p
-regularity in these spaces for p ∈ (1,∞). In this paper we show that ɛ + A has a bounded H
∞-calculus in for all q ∈ (1, ∞) and ɛ > 0. This allows to identify domains of fractional powers of the Stokes operator.
Received: 12 October 2007 相似文献
17.
For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues
denote by E(λi; T) the eigen-projection corresponding to an eigenvalue λi. In this paper we will show that if the operator sequence
is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators Tp and Tr: T = Tp + Tr, where Tp is the weak limit of Tn and Tr is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body. 相似文献
18.
In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < q < p* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that,
when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively
first or second eigenfunctions of −Δ
p
.
Received: 29 April 2008 相似文献
19.
C. Buşe A. D. R. Choudary S. S. Dragomir M. S. Prajea 《Integral Equations and Operator Theory》2008,61(3):325-340
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family defined on a Banach space and satisfying some measurability conditions is uniformly exponentially stable if and only if for
some 1 ≤ p < ∞, we have that:
Actually the Barbashin result was formulated for non-autonomous differential equations in the framework of finite dimensional
spaces. Here we replace the above ”uniform” condition be a ”strong” one.
Among others we shall prove that the evolution family is uniformly exponentially stable if there exists a non-decreasing function with for all r > 0 such that for each , one has:
In particular, the family U is uniformly exponentially stable if and only if for some 0 < p < ∞ and each , the inequality
is fulfilled. The latter result extends a similar one from the recent paper [4]. Related results for periodic evolution families
are also obtained.
相似文献
20.
We consider the Schr?dinger operator Hγ = ( − Δ)l + γ V(x)· acting in the space
$$L_2 (\mathbb{R}^d ),$$ where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
$$\lim _{|{\mathbf{x}}| \to \infty } V({\mathbf{x}}) = 0.$$ We obtain an asymptotic expansion as
$$\gamma \uparrow 0$$of the bottom negative eigenvalue of Hγ, which is born at the moment γ = 0 from the lower bound λ = 0 of the spectrum σ(H0) of the unperturbed operator H0 = ( − Δ)l (a virtual eigenvalue). To this end we develop a supplement to the Birman-Schwinger theory on the process of the birth of
eigenvalues in the gap of the spectrum of the unperturbed operator H0. Furthermore, we extract a finite-rank portion Φ(λ) from the Birman- Schwinger operator
$$X_V (\lambda ) = V^{\frac{1} {2}} R_\lambda (H_0 )V^{\frac{1}{2}} ,$$ which yields the leading terms for the desired asymptotic
expansion. 相似文献