Hiroshima Mathematical Journal

On the asymptotics of solutions for some Schrödinger equations with dissipative perturbations of rank one

Mitsuteru Kadowaki, Hideo Nakazawa, and Kazuo Watanabe

Full-text: Open access

Abstract

The classification of solutions for some dissipative systems by the information of the spectrum is established. Its generator is non self-adjoint Schrödinger operator with rank one singular perturbation. For the proof, a generalized Parseval formula is constructed.

Article information

Source
Hiroshima Math. J., Volume 34, Number 3 (2004), 345-369.

Dates
First available in Project Euclid: 22 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1150998510

Digital Object Identifier
doi:10.32917/hmj/1150998510

Mathematical Reviews number (MathSciNet)
MR2120520

Zentralblatt MATH identifier
1078.35099

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics
Secondary: 35P10: Completeness of eigenfunctions, eigenfunction expansions 35P25: Scattering theory [See also 47A40] 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx] 81Q05: Closed and approximate solutions to the Schrödinger, Dirac, Klein- Gordon and other equations of quantum mechanics

Citation

Kadowaki, Mitsuteru; Nakazawa, Hideo; Watanabe, Kazuo. On the asymptotics of solutions for some Schrödinger equations with dissipative perturbations of rank one. Hiroshima Math. J. 34 (2004), no. 3, 345--369. doi:10.32917/hmj/1150998510. https://projecteuclid.org/euclid.hmj/1150998510


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