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Lp‐Theory for Schrödinger systems

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  • M. Kunze
  • L. Lorenzi
  • A. Maichine
  • A. Rhandi

Abstract

In this article, we study for p∈(1,∞) the Lp‐realization of the vector‐valued Schrödinger operator Lu:= div (Q∇u)+Vu. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the Lp‐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 Lp(Rd;Cm). We also study additional properties of the semigroup such as extension to L1, positivity, ultracontractivity and prove that the generator has compact resolvent.

Suggested Citation

  • M. Kunze & L. Lorenzi & A. Maichine & A. Rhandi, 2019. "Lp‐Theory for Schrödinger systems," Mathematische Nachrichten, Wiley Blackwell, vol. 292(8), pages 1763-1776, August.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:8:p:1763-1776
    DOI: 10.1002/mana.201800206
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