Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10556/3131
Titolo: On Vector-Valued Schrodinger Operators in Lp-spaces
Autore: Maichine, Abdallah
Scarpa, Roberto
Rhandi, Abdelaziz
Parole chiave: Schrodinger
Semigroup
Data: 6-apr-2018
Editore: Universita degli studi di Salerno
Abstract: ... We construct a realization Ap of A in the spaces Lp(Rd;Cm), 1 p < 1, that generates a contractive strongly continuous semigroup. First, by using form methods, we obtain generation of holomorphic semigroups when the potential V is symmetric. In the general case, we use some other techniques of functional analysis and operator theory to get a m-dissipative realization. But in this case the semigroup is not, in general, analytic. We characterize the domain of the operator Ap in Lp(Rd;Cm) by using rstly a non commutative version of the Dore-Venni theorem and then a perturbation theorem due to Okazawa. We discuss some properties of the semigroup such as analyticity, compactness and positivity. We establish ultracontractivity and deduce that the semigroup is given by an integral kernel. Here, the kernel is actually a matrix whose entries satisfy Gaussian upper estimates. Further estimates of the kernel entries are given for potentials with a diagonal of polynomial growth. Suitable estimates lead to the asymptotic behavior of the eigenvalues of the matrix Schr odinger operator when the potential is symmetric. [edited by Author]
Descrizione: 2016 - 2017
URI: http://hdl.handle.net/10556/3131
http://dx.doi.org/10.14273/unisa-1404
È visualizzato nelle collezioni:Matematica, Fisica ed Applicazioni

File in questo documento:
File Descrizione DimensioniFormato 
tesi_di_dottorato_A_Maichine.pdftesi di dottorato1,02 MBAdobe PDFVisualizza/apri
abstract_in_inglese_A_Maichine.pdfabstract in inglese a cura dell'autore109,41 kBAdobe PDFVisualizza/apri
abstract_in_italiano_A_Maichine.pdfabstract in italiano a cura dell'autore100,02 kBAdobe PDFVisualizza/apri


Tutti i documenti archiviati in DSpace sono protetti da copyright. Tutti i diritti riservati.