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# Documents  Rhandi, Abdelaziz | enregistrements trouvés : 2

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## $L^p$-theory for Schrödinger systems Rhandi, Abdelaziz | CIRM H

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Research talks

In this talk we study for $p\in \left ( 1,\infty \right )$ the $L^{p}$-realization of the vector-valued Schrödinger operator $\mathcal{L}u:= div\left ( Q\triangledown u \right )+Vu$. Using a noncommutative version of the Dore-Venni theorem due to Monniaux and Prüss, and a perturbation theorem by Okazawa, we prove that $L^{p}$, the $L^{p}$-realization of $\mathcal{L}$, defined on the intersection of the natural domains of the differential and multiplication operators which form $\mathcal{L}$, generates a strongly continuous contraction semigroup on $L^{p}\left ( \mathbb{R}^{d} ;\mathbb{C}^{m}\right )$. We also study additional properties of the semigroup such as positivity, ultracontractivity, Gaussian estimates and compactness of the resolvent. We end the talk by giving some generalizations obtained recently and several examples. In this talk we study for $p\in \left ( 1,\infty \right )$ the $L^{p}$-realization of the vector-valued Schrödinger operator $\mathcal{L}u:= div\left ( Q\triangledown u \right )+Vu$. Using a noncommutative version of the Dore-Venni theorem due to Monniaux and Prüss, and a perturbation theorem by Okazawa, we prove that $L^{p}$, the $L^{p}$-realization of $\mathcal{L}$, defined on the intersection of the natural domains of the differential and ...

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## Positive operator semigroups:from finite to infinite dimensions Batkai, Andras ; Kramar Fijavz, Marjeta ; Rhandi, Abdelaziz | Birkhäuser 2017

Ouvrage

- xvii; 364 p.
ISBN 978-3-319-42811-6

Operator theory: advances and applications , 0257

Localisation : Collection 1er étage

semi-groupe d'opérateurs # théorie de Perron-Frobenius # matrice graphique # modèle de population structuré selon l'âge # modèle économique # transport de neutrons # équation de retard

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