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A Stationary Approach to the Scattering on Noncompact Star Graphs Containing Finite Rays

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

In this paper we consider Schrödinger operators on noncompact star-shaped graphs including some finite rays. We show that our spectral representation formula provides the time dependent formulation of the scattering theory. The scattering operator S is constructed in the configuration space, and then is related to the scattering matrix S(λ) in the momentum space. Corresponding inverse scattering problem is investigated.

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Acknowledgement

The first author was partly supported by Grant-in-Aid for Scientific Research (C) (Nos. 22540204, 23540181), Japan Society for the Promotion of Science. The second author was partly supported by Grant-in-Aid for Scientific Research (C) (No. 23540181), Japan Society for the Promotion of Science.

Author information

Authors and Affiliations

  1. Department of Mathematics, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Kiyoshi Mochizuki

  2. Emeritus, Tokyo Metropolitan University, Tokyo, Japan

    Kiyoshi Mochizuki

  3. Institute of International Education, Tohoku University, Kawauchi, Aoba, Sendai, Miyagi, 980-8576, Japan

    Igor Trooshin

Authors
  1. Kiyoshi Mochizuki
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  2. Igor Trooshin
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Corresponding author

Correspondence to Kiyoshi Mochizuki .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Mochizuki, K., Trooshin, I. (2015). A Stationary Approach to the Scattering on Noncompact Star Graphs Containing Finite Rays. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_30

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