L p -spaces]]>

摘要

In the paper theLp-realizationLpof the matrix Schr?dinger operatorLu=div(Q?u)+Vuwas studied. The generation of a semigroup inLp(Rd,Cm)and characterization of the domainD(Lp)has been established. In this paper we perturb the operatorLpby a scalar potential belonging to a class including all polynomials and show that still we have a strongly continuous semigroup onLp(Rd,Cm)with domain embedded inW2,p(Rd,Cm). We also study the analyticity, compactness, positivity and ultracontractivity of the semigroup and prove Gaussian kernel estimates. Further kernel estimates and asymptotic behaviour of eigenvalues of the matrix Schr?dinger operator are investigated.