Let Hk(Z2) denote the semigroup of linear operators on Mk(Z2), the spaceof all k×k matrices, over Z2 that are invertible and preserve involutory matrices. The mainresult is that the structure of semigroup Hk(Z2) is determined.
The article has proved the conclusion as follows:Let sernigroup S =R×L is direct product of semigroup R and L. then for all subsemigroup T of S, there exists subsemigroup Rf and L' of R and L, such that T=R'× L',if and only if S is the direct product of a rectangular band and a periodic group.
In this paper, we establish maximal Lp-Lq estimates for non-autonomous parabolic equations of the type u'(t)+A(t)u(t)=f(t), u(0)=0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t∈[0,T].
In this paper, by using the theory of semigroup and spectrum, a computation formula on the growth order of one class ofC0-semigroups in Banach space is proved.
This new type of inequality not only implies heat kernel bounds as the classical Li-Yau's Harnack inequality did, but also provides a direct way to describe various dimension-free properties of finite and infinite-dimensional diffusion semigroups.
We mainly focus on the applications of skew convolution semigroups and the connections in those processes.
Isomorphic embeddability of semigroups with countable sets of defining relations in finitely defined semigroups
For an arbitrary abstract theoretico-semi-group propertyθ, satisfying certain natural conditions, we describe (to within the structure of groups possessing the propertyθ) the structure of periodic subgroups with the propertyθ.
Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained.
A linear semi-group for both: Markov processes and non-Markov processes as they occur in the description of macroscopic systems is introduced.
In this context, a semi-group formulation for the validity of various expansion methods of master equations developed recently is given and the convergence of functionals of the original process to a limiting transformed process is investigated.
In this paper, we shall introduce the concept of the Bessel (Riesz) potential K?the function spacesXs (Xs) and give some dual estimates for a class of operators determined by a semi-group in the spacesLq (-T, T; Xs) (Lq(-T, T; Xs)).