Dispersive estimate for the Schrödinger equation with point interactions | Zendy

D'Ancona Piero | Zendy; Pierfelice Vittoria | Zendy; Teta Alessandro | Zendy

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Dispersive estimate for the Schrödinger equation with point interactions

Author(s) -

D'Ancona Piero,

Pierfelice Vittoria,

Teta Alessandro

Publication year - 2006

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.682

Subject(s) - resolvent , mathematics , operator (biology) , unitary state , schrödinger's cat , point (geometry) , flow (mathematics) , schrödinger equation , mathematical physics , unitary group , mathematical analysis , pure mathematics , geometry , law , biochemistry , chemistry , repressor , political science , transcription factor , gene

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. Copyright © 2005 John Wiley & Sons, Ltd.

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