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Journal of Functional Analysis 245 (2007) 213248 www.elsevier.com/locate/jfa

Summary: Journal of Functional Analysis 245 (2007) 213­248
Ground-state positivity, negativity, and compactness
for a Schrödinger operator in RN
Bénédicte Alziary a
, Jacqueline Fleckinger-Pellé a
, Peter Takác b,,1
a Université Toulouse 1 (Sciences Sociales), CEREMATH-UMR MIP, 21 Allées de Brienne,
F-31000 Toulouse Cedex, France
b Universität Rostock, Fachbereich Mathematik, Universitätsplatz 1, D-18055 Rostock, Germany
Received 6 November 2006; accepted 5 December 2006
Available online 31 January 2007
Communicated by L. Gross
We treat the Schrödinger operator A = - + q(x)ˇ on L2(RN ) with the potential q :RN [q0,)
bounded below and satisfying some reasonable hypotheses on the growth at infinity (faster than |x|2 as
|x| ). We are concerned primarily with the compactness of the resolvent (A - I)-1 of A as an
operator on the Banach space X,
X = f L2 RN : f/ L RN , f X = esssup


Source: Alziary-Chassat, Bénédicte - Université Toulouse 1 - Capitole


Collections: Mathematics