Characterizations Of A Class Of Convolution Semi-group Martin Border

In 1966,Ney.P and F.Spiter gave a description of Martin boundary in [1], the main result in this article is the following:Let Zn={x ∈ Rn : x = (x1,x2,…,xn),xl ∈ Z,1≤i≤n}. p is a transition function on Zn ,it satisfies0≤p(x,y) = p(0,y-x),x,y ∈ Zn,(0,x)=1.We can define pn by p P0(x,y)=1,asx=y,othewise 0. pn+1(x,y)=pn (x, z)p(z, y),n≥0Let u ∈D,q= |gradφ(u)|xn∈Zn, and|xn|,If potential kernel G(x,y) = pn(x,y) is transient,then lim then lim There is a description of Martin boundary above for random walk, then we can answer if there is a description of Martin boundary as above for continuous time parameter process. This article studies a continuous time parameter semigroup with a drift and obtain a resultas following: Let B(Rn) be Borel σ-algebra on Rn,B(Rn)={A ∈ B(Rn): closure of A is compact}, {πt;t >0} is a convolutoin semigroup on Rn-1, μ1 =π1 εt,t>0. Obviously, {μt} a convolution semigroup on Rn. Define Let , then Eσ iscalled Martin boundary of the convolutoin semigroup Define Thoerem Suppose satisfies the fundmental supposition in the section of 3.2 3, denotes Lebesgue measure). Let Eσ be Martinboundary of{μt}, u E , a=grad(u) , then lim...