TY - JOUR
T1 - Schatten class conditions for functions of Schrodinger operators
AU - Frank, Rupert L.
AU - Pushnitski, Alexander
PY - 2019/11/1
Y1 - 2019/11/1
N2 - We consider the difference f(H1)−f(H0), where H0=−Δ and H1=−Δ+V are the free and the perturbed Schrödinger operators in L2(Rd), respectively, in which V is a real-valued short range potential. We give a sufficient condition for this difference to belong to a given Schatten class Sp, depending on the rate of decay of the potential and on the smoothness of f (stated in terms of the membership in a Besov class). In particular, for p>1 we allow for some unbounded functions f.
AB - We consider the difference f(H1)−f(H0), where H0=−Δ and H1=−Δ+V are the free and the perturbed Schrödinger operators in L2(Rd), respectively, in which V is a real-valued short range potential. We give a sufficient condition for this difference to belong to a given Schatten class Sp, depending on the rate of decay of the potential and on the smoothness of f (stated in terms of the membership in a Besov class). In particular, for p>1 we allow for some unbounded functions f.
UR - http://www.scopus.com/inward/record.url?scp=85073614824&partnerID=8YFLogxK
U2 - 10.1007/s00023-019-00838-8
DO - 10.1007/s00023-019-00838-8
M3 - Article
AN - SCOPUS:85073614824
SN - 1424-0637
VL - 20
SP - 3543
EP - 3562
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 11
ER -