TY - JOUR
T1 - Two-dimensional Schrödinger operators with point interactions
T2 - Threshold expansions, zero modes and Lp -boundedness of wave operators
AU - Cornean, Decebal Horia
AU - Michelangeli, Alessandro
AU - Yajima, Kenji
PY - 2019/5/1
Y1 - 2019/5/1
N2 - We study the threshold behavior of two-dimensional Schrödinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the operator is of regular type, or it has singularities associated with s or p-wave resonances or even with an embedded eigenvalue at zero, for whose existence we give necessary and sufficient conditions. An embedded eigenvalue at zero may appear only if we have at least three centers. When the operator is of regular type, we prove that the wave operators are bounded in Lp(R
2) for all 1 < p < ∞. With a single center, we always are in the regular type case.
AB - We study the threshold behavior of two-dimensional Schrödinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the operator is of regular type, or it has singularities associated with s or p-wave resonances or even with an embedded eigenvalue at zero, for whose existence we give necessary and sufficient conditions. An embedded eigenvalue at zero may appear only if we have at least three centers. When the operator is of regular type, we prove that the wave operators are bounded in Lp(R
2) for all 1 < p < ∞. With a single center, we always are in the regular type case.
KW - L p -boundedness of wave operators
KW - Two-dimensional point interaction
KW - embedded eigenvalue at threshold
KW - resonances at threshold
KW - threshold expansion
UR - http://www.scopus.com/inward/record.url?scp=85057388490&partnerID=8YFLogxK
U2 - 10.1142/S0129055X19500120
DO - 10.1142/S0129055X19500120
M3 - Journal article
SN - 0129-055X
VL - 31
JO - Reviews in Mathematical Physics
JF - Reviews in Mathematical Physics
IS - 4
M1 - 1950012
ER -