### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

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

**Inverse problem and singularity of the integration kernel.** / Gang, Hu; Ning, Cun-Zheng; Haken, H.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 205, no. 2-3, pp. 130-136. https://doi.org/10.1016/0375-9601(95)00544-D

}

TY - JOUR

T1 - Inverse problem and singularity of the integration kernel

AU - Gang, Hu

AU - Ning, Cun-Zheng

AU - Haken, H.

PY - 1995/9/11

Y1 - 1995/9/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58149324876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149324876&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(95)00544-D

DO - 10.1016/0375-9601(95)00544-D

M3 - Article

AN - SCOPUS:58149324876

VL - 205

SP - 130

EP - 136

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2-3

ER -