## The spectrum of differential operators with almost constant coefficients II

Autor(en): | Behncke, H |

Stichwörter: | EQUATIONS; Mathematics; Mathematics, Applied; POTENTIALS; SCHRODINGER-OPERATORS; SYSTEMS |

Erscheinungsdatum: | 2002 |

Herausgeber: | ELSEVIER SCIENCE BV |

Journal: | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS |

Volumen: | 148 |

Ausgabe: | 1 |

Startseite: | 287 |

Seitenende: | 305 |

Zusammenfassung: | The absolutely continuous spectrum of differential operators of the form Ly = w(-1)Sigma(k=0)(n)(-1)(k)(p(k)y((k)))((k)) on L-2([9, infinity), w) is determined. With p(n)(x), w(x) > 0 the coefficients p(k) are assumed to satisfy (p) over tilde (k) (x) = (p(k) y(2k)w(-1))(x) --> c(k), y = (w (.) p(n)(-1))(1/2n). If the coefficients satisfy some additional smoothness and decay conditions, the absolutely continuous part H-ac of any self-adjoint extension of L is unitarily equivalent to the operator of multiplication by P(x) = Sigma(0)(n) c(k)x(2k) on L-2([0, infinity)). Several extensions of this result as well as examples are shown. (C) 2002 Elsevier Science B.V. All rights reserved. |

ISSN: | 03770427 |

DOI: | 10.1016/S0377-0427(02)00586-1 |

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