## Abstract

We will consider the indefinite multidimensional truncated moment problem. Necessary and sufficient conditions for a given truncated multisequence to have a signed representing measure with minimal cardinality of its support are given by the existence of a rank preserving extension of a multivariate Hankel matrix (built from the given truncated multisequence) such that the corresponding associated polynomial ideal is real radical. This result is a special case of a more general characterisation of truncated multisequences with a minimal complex representing measure whose support is symmetric with respect to complex conjugation (which we will call quasi-complex). One motivation for our results is the fact that positive semidefinite truncated multisequences need not have a positive representing measure. Thus, our main result gives the potential for computing a signed representing measure μ with Jordan decomposition μ=μ_{+}−μ_{−}, where cardμ_{−} is small. We will illustrate this point on concrete examples.

Original language | English |
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Article number | 125091 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 500 |

Issue number | 1 |

DOIs | |

State | Published - 1 Aug 2021 |

Externally published | Yes |

## Keywords

- Indefinite moment problem
- Pontryagin space
- Signed representing measure
- Truncated moment problem

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics