We consider the Schrödinger operator in ℝ^3 with N point interactions placed at Y=(y_1,…,y_N), y_j ∈ ℝ^3, of strength α=(α_1,…,α_N), α_j ∈ ℝ. Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove the (weighted) dispersive estimate for the corresponding Schrödinger flow. In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form.

Dispersive estimate for the Schroedinger equation with point interactions / D'Ancona, Piero Antonio; V., Pierfelice; Teta, Alessandro. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 29:3(2006), pp. 309-323. [10.1002/mma.682]

Dispersive estimate for the Schroedinger equation with point interactions.

D'ANCONA, Piero Antonio;TETA, Alessandro
2006

Abstract

We consider the Schrödinger operator in ℝ^3 with N point interactions placed at Y=(y_1,…,y_N), y_j ∈ ℝ^3, of strength α=(α_1,…,α_N), α_j ∈ ℝ. Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove the (weighted) dispersive estimate for the corresponding Schrödinger flow. In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form.
2006
resolvent estimates, decay estimates, dispersive equations, Schrödinger equation
01 Pubblicazione su rivista::01a Articolo in rivista
Dispersive estimate for the Schroedinger equation with point interactions / D'Ancona, Piero Antonio; V., Pierfelice; Teta, Alessandro. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 29:3(2006), pp. 309-323. [10.1002/mma.682]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/518383
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