On a polynomial scalar perturbation of a Schr "odinger system in\n L^p-spaces

2018/02/08 by Abdallah Maichine, Maichine, Abdallah, Abdelaziz Rhandi +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1802.02772

Abstract

In the paper citeKLMR the L^p-realization L_p of the matrix\nSchr "odinger operator \Lu=div(Q\∇ u)+Vu was studied. The\ngeneration of a semigroup in L^p( R^d, C^m) and characterization of the\ndomain D(L_p) has been established. In this paper we perturb the operator\nL_p of by a scalar potential belonging to a class including all polynomials\nand show that still we have a strongly continuous semigroup on L^p( R^d, C^m)\nwith domain embedded in W^2,p( R^d, C^m). We also study the analyticity,\ncompactness, positivity and ultracontractivity of the semigroup and prove\nGaussian kernel estimates. Further kernel estimates and asymptotic behaviour of\neigenvalues of the matrix Schr "odinger operator are investigated.\n

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