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ARTICLE IN PRESS YJFAN:5529 Please cite this article in press as: B. Alziary, P. Takc, Intrinsic ultracontractivity of a Schrdinger semigroup in RN ,
 

Summary: ARTICLE IN PRESS YJFAN:5529
Please cite this article in press as: B. Alziary, P. Takác, Intrinsic ultracontractivity of a Schrödinger semigroup in RN ,
J. Funct. Anal. (2009), doi:10.1016/j.jfa.2009.02.013
JID:YJFAN AID:5529 /FLA [m1+; v 1.110; Prn:3/03/2009; 14:57] P.1 (1-33)
Journal of Functional Analysis ˇˇˇ (ˇˇˇˇ) ˇˇˇ­ˇˇˇ
www.elsevier.com/locate/jfa
Intrinsic ultracontractivity of a Schrödinger
semigroup in RN
Bénédicte Alziary 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 7 October 2008; accepted 23 February 2009
Communicated by C. Kenig
Abstract
We give a (possibly sharp) sufficient condition on the electric potential q :RN [0,) in the
Schrödinger operator A = - + q(x)ˇ on L2(RN ) that guarantees that the Schrödinger heat semigroup
{e-At : t 0} on L2(RN ) generated by -A is intrinsically ultracontractive. Moreover, if q(x) q(|x|) is
radially symmetric, we show that our condition on q is also necessary (i.e., truly sharp); it reads

  

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

 

Collections: Mathematics