共查询到20条相似文献,搜索用时 70 毫秒
1.
Gerd Rodé 《Semigroup Forum》1983,26(1):317-321
It is proved that each continuous semigroup {P(t)}t≥0 of convex operators P(t):Rn→Rn is continuously differentiable with respect to t.
This note represents a first step towards a better understanding of semigroups formed by convex operators. We establish the
differentiability of a convex semigroup in the finite dimensional case, generalizing a basic result from linear semigroup
theory.
Our motivation for the study of semigroups of convex operators comes from the theory of Markov decision processes. In [1]
and in [2] it was shown that the maximum reward of these processes can be described by a certain nonlinear semigroup. The
nonlinear operators are defined as suprema of linear operators (plus a constant), hence they are convex operators.
It seems that the convexity assumption keeps its smoothing influence even in the infinite dimensional situation. We hope to
discuss this in a future paper. 相似文献
2.
一类无穷维Hamilton算子的半群生成定理 总被引:3,自引:0,他引:3
研究了无穷维H am ilton算子生成C0半群的问题,得到了类无穷维H am ilton算子生成C0半群的一个充分条件.把结果应用在一类双曲型混合问题生成的无穷维H am ilton算子上,证明此类算子生成C0半群,并利用H ille-Y osida定理进一步说明了结果的正确性和有效性.另外,还给出了波动方程相应的无穷维H am ilton算子所生成的C0半群的具体表达式. 相似文献
3.
Markus Kunze 《Czechoslovak Mathematical Journal》2011,61(2):437-459
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type
integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study
a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give
conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel
operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform. 相似文献
4.
Luigi Manca 《Journal of Evolution Equations》2008,8(2):231-262
We consider a semigroup of operators in the Banach space C
b
(H) of uniformly continuous and bounded functions on a separable Hilbert space H. We prove an existence and uniqueness result for a measure valued equation involving this class of semigroups. Then we apply
the result to the transition semigroup and the Kolmogorov operator corresponding to a stochastic PDE in H. For this purpose, we characterize the generator of the transition semigroup on a core.
相似文献
5.
研究有界线性算子强连续半群在非线性Lipschitz扰动下的正则性质保持问题.具体地,我们证明:如果强连续半群是直接范数连续的,则非线性扰动半群是直接Lipschitz范数连续的.结论推广了线性算子半群的范数连续性质保持,丰富和完善了非线性算子半群的理论. 相似文献
6.
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of self-adjoint semigroups of partial isometries. We obtain a general structure result showing that every self-adjoint semigroup of partial isometries consists of “generalized weighted composition” operators on a space of square-integrable Hilbert-space valued functions. If the semigroup is finitely generated then the underlying measure space is purely atomic, so that the semigroup is represented as “zero-unitary” matrices. The same is true if the semigroup contains a compact operator, in which case it is not even required that the semigroup be self-adjoint. 相似文献
7.
This paper studies semigroups of operators on Hardy and Dirichlet spaces whose generators are differential operators of order greater than one. The theory of forms is used to provide conditions for the generation of semigroups by second order differential operators. Finally, a class of more general weighted Hardy spaces is considered and necessary and sufficient conditions are given for an operator of the form \(f \mapsto Gf^{(n_0)}\) (for holomorphic G and arbitrary \(n_0\)) to generate a semigroup of quasicontractions. 相似文献
8.
A. R. Mirotin 《Siberian Mathematical Journal》2001,43(1):114-123
We give some conditions on functions of the Schoenberg class T for them to send the generators of uniformly bounded semigroup of class C 0 to the generators of holomorphic semigroups. This generalizes Yosida, Balakrishnan, and Kato's result relating to fractional powers of operators. The functional calculus of generators of C 0-semigroups which uses the class T was constructed in the preceding articles of the author. 相似文献
9.
We give some conditions on functions of the Schoenberg class T for them to send the generators of uniformly bounded semigroup of class C
0 to the generators of holomorphic semigroups. This generalizes Yosida, Balakrishnan, and Kato's result relating to fractional powers of operators. The functional calculus of generators of C
0-semigroups which uses the class T was constructed in the preceding articles of the author. 相似文献
10.
Sen-Yen Shaw 《Journal of Functional Analysis》1982,49(2):152-169
The aim of this paper is to study ergodic properties (i.e., properties about the limit of Cesàro averages) of a semigroup of bounded linear operators on a Banach space X, which is assumed to be continuous and locally integrable in the sense of a certain general weak topology of X. Then the results are applied to particular examples, such as locally strongly integrable semigroups, their dual semigroups, and the tensor product semigroup of two (C0)-semigroups. 相似文献
11.
Michael Röckner 《Journal of Functional Analysis》2003,203(1):237-261
Harnack inequalities are established for a class of generalized Mehler semigroups, which in particular imply upper bound estimates for the transition density. Moreover, Poincaré and log-Sobolev inequalities are proved in terms of estimates for the square field operators. Furthermore, under a condition, well-known in the Gaussian case, we prove that generalized Mehler semigroups are strong Feller. The results are illustrated by concrete examples. In particular, we show that a generalized Mehler semigroup with an α-stable part is not hyperbounded but exponentially ergodic, and that the log-Sobolev constant obtained by our method in the special Gaussian case can be sharper than the one following from the usual curvature condition. Moreover, a Harnack inequality is established for the generalized Mehler semigroup associated with the Dirichlet heat semigroup on (0,1). We also prove that this semigroup is not hyperbounded. 相似文献
12.
Ernie Manes 《Semigroup Forum》2006,72(1):94-120
The variety of guarded semigroups consists of all (S,·, ˉ) where (S,·) is a semigroup and x ↦ \overline{x} is a unary operation
subject to four additional equations relating it to multiplication. The semigroup Pfn(X) of all partial transformations on
X is a guarded semigroup if x \overline{f} = x when xf is defined and is undefined otherwise. Every guarded semigroup is
a subalgebra of Pfn(X) for some X. A covering theorem of McAlister type is obtained. Free guarded semigroups are constructed
paralleling Scheiblich's construction of free inverse semigroups. The variety of banded semigroups has the same signature
but different equations. There is a canonical forgetful functor from guarded semigroups to banded semigroups. A semigroup
underlies a banded semigroup if and only if it is a split strong semilattice of right zero semigroups. Each banded semigroup
S contains a canonical subsemilattice g⋆(S). For any given semilattice L, a construction to synthesize the general banded semigroup S with g⋆ ≅ L is obtained. 相似文献
13.
Lassi Paunonen 《Journal of Functional Analysis》2012,263(9):2555-2583
In this paper we study the robustness properties of strong and polynomial stability of semigroups of operators. We show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator. The presented results apply to general polynomially stable semigroups and bounded perturbations. The conditions on the perturbations generalize well-known criteria for the preservation of exponential stability of semigroups. We also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a Riesz-spectral operator. The theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one-dimensional wave equation. 相似文献
14.
A. R. Mirotin 《Siberian Mathematical Journal》2011,52(6):1032-1041
We develop the multidimensional functional calculus of semigroup generators which is based on the class of Bernstein functions
in several variables. We establish spectral mapping theorems, give a holomorphy condition for the semigroups generated by
the operators arising in this calculus, as well as prove the moment inequality for these operators. 相似文献
15.
Barry Simon 《Journal of Functional Analysis》1973,12(3):335-339
We prove that an ergodic semigroup of positivity preserving self-adjoint operators is positivity improving. We also present a new proof (using Markov techniques) of the ergodicity of semigroups generated by spatially cutoff P(?)2 Hamiltonians. 相似文献
16.
As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated
by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in
on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W
U
and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known
result of El-Qallali and Fountain for type W semigroups.
This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation
of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123) 相似文献
17.
We derive new necessary and sufficient conditions for admissibility
of observation operators for certain C
0-semigroups. We also prove a new
sufficient criterion for admissibility for observation operators with infinite-dimensional
output space on contraction semigroups. If the contraction semigroup
is completely non-unitary and its co-generator has finite defect indices,
then this criterion is also necessary. In the case of the right shift semigroup
on L
2(0,), these conditions translate into conditions for the boundedness
of Hankel operators. 相似文献
18.
A. V. Zhuchok 《Mathematical Notes》2018,103(5-6):737-744
The present paper is devoted to the study of n-tuple semigroups. A free n-tuple semigroup of arbitrary rank is constructed and, as a consequence, singly generated free n-tuple semigroups are characterized. Moreover, examples of n-tuple semigroups are presented, the independence of the n-tuple semigroup axioms is proved, and it is shown that the natural semigroups of the constructed free n-tuple semigroup are isomorphic and the automorphism group of this n-tuple semigroup is isomorphic to a symmetric group. 相似文献
19.
Prof. M. L. Silverstein 《Probability Theory and Related Fields》1969,14(2):96-112
Summary This paper is concerned with Markov processes with continuous creation where the phase space is a general separable compact metric space. The transition probabilities for such a process determine a semigroup of operators acting on a function space over the collection of bounded Borel measures on the phase space. Such a semigroup is characterized by a particular convolution condition and is called a continuous state branching semigroup. A connection is established between continuous state branching semigroups and certain semigroups of nonlinear operators and then this connection is exploited to establish an existence theorem for the former.Research associated with a project in probability at Princeton University supported by the Office of Army Research. 相似文献
20.