## Abstract

Let -Domega((.), z)D + q be a differential operator in L-2(0, infinity) whose leading coefficient contains the eigenvalue parameter z. For the case that omega((.), z) has the particular form

omega(t, z) = p(t) + c(t)(2)/(z - r (t)), z is an element of C \ R,

and the coefficient functions satisfy certain local integrability conditions, it is shown that there is an analog for the usual limit-point/limit-circle classification. In the limit-point case mild sufficient conditions are given so that all but one of the Titchmarsh-Weyl coefficients belong to the so-called Kac subclass of Nevanlinna functions. An interpretation of the Titchmarsh-Weyl coefficients is given also in terms of an associated system of differential equations where the eigenvalue parameter appears linearly. (C) 2004 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 258-275 |

Number of pages | 18 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 295 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1-Jul-2004 |

## Keywords

- floating singularity
- Sturm-Liouville operator
- Titchmarsh-Weyl coefficient
- limit-point/limit-circle
- Kac class
- symmetric operator
- self-adjoint extension
- OPERATORS