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Applied Analysis
Seminar information archive ～12/08｜Next seminar｜Future seminars 12/09～
| Date, time & place | Thursday 16:00 - 17:30 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, MIYAMOTO Yasuhito, MITAKE Hiroyoshi, TAKADA Ryo |
2011/06/09
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kiyoshi Mochizuki (Tokyo Metropolitan University, Emeritus Professor)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
Kiyoshi Mochizuki (Tokyo Metropolitan University, Emeritus Professor)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
[ Abstract ]
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
