Resolvent Estimates and Matrix-Valued Schrödinger Operator with Eigenvalue Crossings; Application to Strichartz Estimates

2008 ◽  
Vol 33 (1) ◽  
pp. 19-44 ◽  
Author(s):  
Clotilde Fermanian Kammerer ◽  
Vidian Rousse
Keyword(s):  
Schrödinger Operator ◽  
Strichartz Estimates ◽  
Schrodinger Operator ◽  
Resolvent Estimates

Low energy resolvent estimates and continuity of time-delay operators

1987 ◽  
Vol 105 (1) ◽  
pp. 229-242 ◽  
Author(s):  
Wang Xue-Ping
Keyword(s):  
Time Delay ◽  
Schrödinger Operator ◽  
Bounded Operator ◽  
Weighted Sobolev Spaces ◽  
Potential Scattering ◽  
Low Energy ◽  
Energy Estimates ◽  
Schrodinger Operator ◽  
Resolvent Estimates ◽  
Delay Operator

SynopsisIn this paper, we are interested in the L2-continuity of the Eisenbud–Wigner time-delay operator in potential scattering theory. Using the ideas due to Jensen–Kato [5], we first establish some low energy estimates on the resolvent of the Schrödinger operator and its derivative in weighted Sobolev spaces. Then applying these results together with the global decay of the wave functions (Lemma 3.2), we show that the Eisenbud–Wigner time-delay operator extends to a bounded operator on L2(Rn) with n ≧ 4, on condition that the potential V(x) decreases as fast as 0(|x | −4−ε) at infinity and that 0 is neither the eigenvalue nor the resonance for the Schrodinger operator –Δ + V for n = 4 or 5.

scholarly journals Resolvent estimates for the magnetic Schrödinger operator in dimensions $$\ge 2$$

2019 ◽  
Vol 33 (2) ◽  
pp. 619-641
Author(s):  
Cristóbal J. Meroño ◽  
Leyter Potenciano-Machado ◽  
Mikko Salo
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Resolvent Estimates ◽  
Magnetic Schrödinger Operator

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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