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Mathematica Slovaca

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Volume 67, Issue 4


Finiteness of the discrete spectrum in a three-body system with point interaction

Kazushi Yoshitomi
  • Department of Mathematics and Information Sciences Tokyo Metropolitan University Minamiohsawa 1-1, Hachioji Tokyo 192-0397 Japan
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Published Online: 2017-07-14 | DOI: https://doi.org/10.1515/ms-2017-0030


In this paper we are concerned with a three-body system with point interaction, which is called the Ter-Martirosian–Skornyakov extension. We locate the bottom of the essential spectrum of that system and establish the finiteness of the discrete spectrum below the bottom. Our work here refines the result of [MINLOS, R. A.: On point-like interaction between n fermions and another particle, Mosc. Math. J. 11 (2011), 113–127], where the semi-boundedness of the operator is obtained.

MSC 2010: Primary 81Q10; Secondary 35J10; 35P05; 81Q15

Keywords: three-body system; Ter-Martirosian–Skornyakov extension; point interaction; discrete spectrum


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About the article

Received: 2015-05-30

Accepted: 2016-03-30

Published Online: 2017-07-14

Published in Print: 2017-08-28

Citation Information: Mathematica Slovaca, Volume 67, Issue 4, Pages 1031–1042, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0030.

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