### Abstract

Many important problems in physics and other sciences can be formulated in terms of the inverse problem of type n(y) = ∝K(y ∥ x)g(x) dx, where g(x) is unknown. We show that this problem can be completely solved for a quite general class of kernel K(y ∥ x) by analytically dilating n(y) and K(y ∥ x) to the complex z plane, and by the analysis of the singularity of the dilated kernel K(z ∥ x). The formalism is also extended to multi-dimensional cases.

Original language | English (US) |
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Pages (from-to) | 130-136 |

Number of pages | 7 |

Journal | Physics Letters A |

Volume | 205 |

Issue number | 2-3 |

DOIs | |

State | Published - Sep 11 1995 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Gang, H., Ning, C-Z., & Haken, H. (1995). Inverse problem and singularity of the integration kernel.

*Physics Letters A*,*205*(2-3), 130-136. https://doi.org/10.1016/0375-9601(95)00544-D