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Antibound States and Exponentially Decaying Sturm–Liouville Potentials
Author(s) -
Eastham M. S. P.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003216
Subject(s) - sturm–liouville theory , integrable system , exponential growth , mathematics , boundary value problem , mathematical physics , neumann boundary condition , dirichlet boundary condition , mathematical analysis , dirichlet distribution , physics , pure mathematics
We consider the Sturm–Liouville equation y ″( x )+{λ− q ( x )} y ( x )=0 (0⩽ x <∞) (1.1) with a boundary condition at x = 0 which can be either the Dirichlet condition y (0)=0 (1.2) or the Neumann condition y ′(0)=0 (1.3) As usual, λ is the complex spectral parameter with 0 ⩽ arg λ < 2π, and the potential q is real‐valued and locally integrable in [0, ∞).