共查询到20条相似文献,搜索用时 46 毫秒
1.
The analytic proof due to M. Itô of the Kesten-Ornstein transience criterion for continuous convolution semigroups of nonnegative contraction measures on a compactly generated Abelian locally compact group has been reworked and given a self-contained form. The new proof still relies on the existence of the equilibrium measure but dispenses with the complete maximum principle. 相似文献
2.
Michele Coti Zelati 《Set-Valued and Variational Analysis》2013,21(1):127-149
From the point of view of longterm dynamics, we study multivalued and single-valued semigroups of operators acting on complete metric spaces. We provide necessary and sufficient conditions for the existence of the global attractor under minimal requirements in terms of continuity of the semigroup. In the case of single-valued semigroups possessing a Lyapunov functional, we exhibit a simple proof of the existence and the characterization of the attractor in terms of the unstable set of stationary points. As an application, we consider the multivalued semigroup generated by the equation ruling the evolution of the specific humidity in a system of moist air, and we prove the existence of a regular global attractor. 相似文献
3.
M. A. Antonets 《Journal of Mathematical Sciences》2000,98(6):629-653
The algebra of generalized Weyl symbols is used in the proof of the continuity of the semigroupexptĤ in the Schwartz space of test functions. Fundamental results on algebras of differentiable Weyl symbols are presented.
New examples of σ-temperate Riemannian metrics are constructed. Such metrics form a basis for construction of algebras of
differentiable Weyl symbols. Conditions for the existence of semigroups of operators, conditions for pseudo-differential operators
to be sectorial, and conditions for the continuity of such semigroups in spaces of test functions and distributions are established.
Initial value problems for second-order differential operators are considered. Bibliography: 16 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 18, 1998, pp. 3–42. 相似文献
4.
We consider the multiple fragmentation equations with polynomially bounded fragmentation rates, both in the discrete and continuous cases. The theory of semigroups of operators on Fréchet spaces is used to produce a simple proof that if moments of all non-negative orders of solutions are initially finite then they remain finite for all future times. Moreover, a class of fragmentation processes is identified in which the existence of the first moment of the initial distribution suffices for the existence of all other moments for positive times. 相似文献
5.
Existence and nonexistence of hypercyclic semigroups 总被引:1,自引:0,他引:1
L. Bernal-Gonzá lez K.-G. Grosse-Erdmann 《Proceedings of the American Mathematical Society》2007,135(3):755-766
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinite-dimensional Banach space that is very different from--and considerably shorter than--the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite-dimensional Fréchet space. This complements recent results due to Bès and Chan. Moreover, we discuss the Hypercyclicity Criterion for semigroups and we give an example of a separable infinite-dimensional locally convex space which supports no supercyclic strongly continuous semigroup of operators.
6.
Karel Pravda-Starov 《Mathematische Zeitschrift》2008,259(2):363-391
We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators
are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We establish
in this paper that under the assumption of ellipticity, as soon as the real part of their Weyl symbols is a non-zero non-positive
quadratic form, the norm of contraction semigroups generated by these operators decays exponentially in time. 相似文献
7.
Peer Christian Kunstmann 《Mathematische Zeitschrift》2002,242(1):183-201
We study -spectral properties of Neumann Laplacians on some planar domains and show by calculation that the essential spectrum of the
Neumann Laplacian on certain horns depends on p. The proof uses ideas due to E.B. Davies and B. Simon for the reduction to one-dimensional operators and techniques involving
Gaussian bounds. For domains looking like comets or stars, i.e. having countably many horn-shaped outlets, we prove a decoupling-reduction
result. These results are used to construct planar domains for which the Neumann Laplacian has maximal -spectrum in the class of generators of symmetric submarkovian semigroups.
Received: 17 January 2000; in final form: 25 July 2000 / Published online: 23 July 2001 相似文献
8.
Michael Demuth Peter Stollmann Günter Stolz Jan van Casteren 《Integral Equations and Operator Theory》1995,23(2):145-153
We give trace norm estimates for products of integral operators and for diffusion semigroups. These are applied to differences of heat semigroups. A natural example of an integral operator with finite trace which is not trace class is given. 相似文献
9.
Zen Harper 《Journal of Evolution Equations》2005,5(3):387-405
We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators
with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported
on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section
3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section
4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture
(for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups
not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness
results for certain convolution operators. 相似文献
10.
The main results of the present paper are related to the use of finite-difference operators for estimating the norms of inverses
of differential operators with unbounded operator coefficients. We obtain a new proof of the Gearhart-Prüss spectral mapping
theorem for operator semigroups in a Hilbert space and estimate the exponential dichotomy exponents of an operator semigroup. 相似文献
11.
In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite
delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated
semigroups and cosine families.
相似文献
12.
Some perturbation results for exponentially dichotomous operators are applied to prove the existence of stable and anti-stable solutions of Riccati equations associated to block operators on general Banach spaces, both for compact perturbations and for bisemigroups made up of immediately norm continuous semigroups. 相似文献
13.
Ramón Bruzual 《Integral Equations and Operator Theory》1993,17(3):301-321
A notion of two-parameter local semigroups of isometric operators in Hilbert space is discussed. It is shown that under certain conditions such a semigroup can be extended to a strongly continuous two-parameter group of unitary operators in a larger Hilbert space. As an application a simple proof of the Eskin bidimensional version of the Krein extension theorem is given. 相似文献
14.
In this paper we study stochastic optimal control problems with jumps with the help of the theory of Backward Stochastic Differential Equations (BSDEs) with jumps. We generalize the results of Peng [S. Peng, BSDE and stochastic optimizations, in: J. Yan, S. Peng, S. Fang, L. Wu, Topics in Stochastic Analysis, Science Press, Beijing, 1997 (Chapter 2) (in Chinese)] by considering cost functionals defined by controlled BSDEs with jumps. The application of BSDE methods, in particular, the use of the notion of stochastic backward semigroups introduced by Peng in the above-mentioned work allows a straightforward proof of a dynamic programming principle for value functions associated with stochastic optimal control problems with jumps. We prove that the value functions are the viscosity solutions of the associated generalized Hamilton–Jacobi–Bellman equations with integral-differential operators. For this proof, we adapt Peng’s BSDE approach, given in the above-mentioned reference, developed in the framework of stochastic control problems driven by Brownian motion to that of stochastic control problems driven by Brownian motion and Poisson random measure. 相似文献
15.
B. V. Rajarama Bhat 《Integral Equations and Operator Theory》2002,42(2):125-141
We obtain existence, uniqueness results for minimal isometric dilations of contractive cocycles of semigroups of unital *-endomorphisms ofB(H. This generalizes the result of Sz. Nagy on minimal isometric dilations of semigroups of contractive operators on a Hilbert space. In a similar fashion we explore results analogus to Sarason's characterization that subspaces to which compressions of semigroups are again semigroups are semi-invariant subspaces, in the context of cocycles and quantum dynamical semigroups.This research is supported by the Indian National Science Academy under Young Scientist Project. 相似文献
16.
O. Kada 《Proceedings of the American Mathematical Society》1999,127(10):3003-3011
We prove strong mean convergence theorems and the existence of ergodic projection and retraction for commutative semigroups of operators which is Eberlein-weakly almost periodic.
17.
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined
in the Weyl quantization by complex-valued quadratic symbols. When the real part of their Weyl symbols is a non-positive quadratic
form, we point out the existence of a particular linear subspace in the phase space intrinsically associated to their Weyl
symbols, called a singular space, such that when the singular space has a symplectic structure, the associated heat semigroup
is smoothing in every direction of its symplectic orthogonal space. When the Weyl symbol of such an operator is elliptic on
the singular space, this space is always symplectic and we prove that the spectrum of the operator is discrete and can be
described as in the case of global ellipticity. We also describe the large time behavior of contraction semigroups generated
by these operators. 相似文献
18.
This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space.
These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second
order partial differential operators generate analytic semigroups inL
p
, 1<p<∞, while the sufficient condition in the other characterization is meaningful in the case of nonlinear operators.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and the National Science Foundation under Grant No.
MCS78-01245. 相似文献
19.
A. V. Balakrishnan 《Applied Mathematics and Optimization》1995,31(2):177-187
In this paper we generalize the Kalman-Yakubovic lemma to infinite dimensions—or, more precisely, to semigroups of operators over a Hilbert space. The proof differs substantially from the finite-dimensional version and is based on the Paley-Wiener-Helson-Lowdenslager factorization theorem. 相似文献
20.
K. Auinger 《Algebra Universalis》1995,34(2):185-190
It is shown that an existence varietyV of regular semigroups contains (all) free products if and only ifV consists solely of locally inverse orE-solid semigroups.Presented by B. M. Schein.The author is indebted to the Australian Research Council for financial support (ARC grant A69231516). 相似文献