In this article we study for p in (1,∞) the L^p-realization of the vector-valued Schroedinger operator Lu:= div(Q∇u) +V u. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Pruess, we prove that the L^p-realization of L, defined on the intersection of the natural domains of the differential and multiplication operators which form L, generates a strongly continuous contraction semigroup on L^p(R^d;C^m). We also study additional properties of the semigroup such as extension to L^1, positivity, ultracontractivity and prove that the generator has compact resolvent.
L^p-theory for Schrödinger systems / Kunze, MARKUS CHRISTIAN; Lorenzi, Luca Francesco Giuseppe; Maichine, Abdallah; Rhandi, Abdelaziz. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 292:8(2019), pp. 1763-1776. [10.1002/mana.201800206]
L^p-theory for Schrödinger systems
KUNZE, MARKUS CHRISTIAN;LORENZI, Luca Francesco Giuseppe;RHANDI, ABDELAZIZ
2019-01-01
Abstract
In this article we study for p in (1,∞) the L^p-realization of the vector-valued Schroedinger operator Lu:= div(Q∇u) +V u. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Pruess, we prove that the L^p-realization of L, defined on the intersection of the natural domains of the differential and multiplication operators which form L, generates a strongly continuous contraction semigroup on L^p(R^d;C^m). We also study additional properties of the semigroup such as extension to L^1, positivity, ultracontractivity and prove that the generator has compact resolvent.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
