### Abstract

M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators. In this note we study such a connection for the function f(t) = 1 − |t|, t - R, which is not positive definite on R: its restrictions fa := f|(−2a,2a) are positive definite if a ≤ 1 and have one negative square if a > 1. We show that with f a canonical differential equation or a Sturm-Liouville equation can be associated which have a singularity.

Original language | English |
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Pages (from-to) | 39-53 |

Number of pages | 15 |

Journal | Methods of Functional Analysis and Topology |

Volume | 10 |

Issue number | 1 |

Publication status | Published - 2004 |

### Keywords

- Hermitian indefinite functions
- canonical systems
- Sturm-Liouville equation

## Cite this

Langer, H., Langer, M., & Sasvári, Z. (2004). Continuations of Hermitian indefinite functions and corresponding canonical systems: an example.

*Methods of Functional Analysis and Topology*,*10*(1), 39-53.