### Abstract

Original language | English |
---|---|

Pages (from-to) | 3403-3420 |

Number of pages | 18 |

Journal | Proceedings A: Mathematical, Physical and Engineering Sciences |

Volume | 460 |

Issue number | 2052 |

DOIs | |

Publication status | Published - Dec 2004 |

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### Keywords

- resonance
- spectral concentration
- embedded eigenvalue
- block operator matrix
- λ-rational eigenvalue problem

### Cite this

*Proceedings A: Mathematical, Physical and Engineering Sciences*,

*460*(2052), 3403-3420. https://doi.org/10.1098/rspa.2003.1272

}

*Proceedings A: Mathematical, Physical and Engineering Sciences*, vol. 460, no. 2052, pp. 3403-3420. https://doi.org/10.1098/rspa.2003.1272

**Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm-Liouville problem.** / Brown, B.Malcolm; Langer, M.; Marletta, Marco.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm-Liouville problem

AU - Brown, B.Malcolm

AU - Langer, M.

AU - Marletta, Marco

PY - 2004/12

Y1 - 2004/12

N2 - This paper studies the resonances and points of spectral concentration of the block operator matrix $$\egin{pmatrix} -\frac{d^2}{d x^2}+q & \sqrt{tw} \\ \sqrt{tw} & u \end{pmatrix} $$ in the space $L^2(0,1) \oplus L^2(0,1)$. In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.

AB - This paper studies the resonances and points of spectral concentration of the block operator matrix $$\egin{pmatrix} -\frac{d^2}{d x^2}+q & \sqrt{tw} \\ \sqrt{tw} & u \end{pmatrix} $$ in the space $L^2(0,1) \oplus L^2(0,1)$. In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.

KW - resonance

KW - spectral concentration

KW - embedded eigenvalue

KW - block operator matrix

KW - λ-rational eigenvalue problem

U2 - 10.1098/rspa.2003.1272

DO - 10.1098/rspa.2003.1272

M3 - Article

VL - 460

SP - 3403

EP - 3420

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2052

ER -