### Abstract

Let G be a homogeneous group with the graded Lie algebra or a noncompact semisimple Lie group with finite center. We define the Fourier transform f of f as a family of operators, and we say that f is positive if all f(n) are positive. Then, we construct an integrable function f on G with positive f and the restriction of f to any ball centered at the origin of G is square-integrable, however, f is not square-integrable on G.

Original language | English |
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Pages (from-to) | 1411-1415 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 123 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1995 May |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Kawazoe, T. (1995). Functions on noncompact lie groups with positive fourier transforms.

*Proceedings of the American Mathematical Society*,*123*(5), 1411-1415. https://doi.org/10.1090/S0002-9939-1995-1277119-7