Finiteness of the discrete spectrum in a three-body system with point interaction
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Kazushi Yoshitomi
Abstract
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.
Acknowledgement
Thanks to the anonymous referees for valuable suggestions and corrections.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Outer measure on effect algebras
- Hamiltonian ordered algebras and congruence extension
- Automorphism groups with some finiteness conditions
- Only finitely many Tribonacci Diophantine triples exist
- Abundant semigroups with a *-normal idempotent
- Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
- Monotonicity results for delta fractional differences revisited
- M-Cantorvals of Ferens type
- Comparison of ψ-porous topologies
- On certain generalized matrix methods of convergence in (ℓ)-groups
- Some applications of first-order differential subordinations
- Hankel determinant for a class of analytic functions involving conical domains defined by subordination
- Nonoscillation and exponential stability of the second order delay differential equation with damping
- Positive solutions of perturbed nonlinear hammerstein integral equation
- Ricci solitons on 3-dimensional cosymplectic manifolds
- Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
- The super socle of the ring of continuous functions
- On the internal approach to differential equations 2. The controllability structure
- Finiteness of the discrete spectrum in a three-body system with point interaction
- On a subclass of Bazilevic functions
