### Abstract

A well-known result of Zygmund states that if ([formula ommitted]) on the circle group T and £ is a Hadamard set of integers, then ([formula ommitted]) In this paper we investigate similar results for the classes ([formula ommitted]) on an arbitrary infinite compact abelian group G and Sidon subsets E of the dual T. These results are obtained as special cases of more general results concerning a new class of lacunary sets([formula ommitted]) where a subset E of ([formula ommitted]). We also prove partial results on the distinctness of the ([formula ommitted]) sets in the index p.

Original language | English |
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Pages (from-to) | 387-403 |

Number of pages | 17 |

Journal | Journal of the Australian Mathematical Society |

Volume | 58 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gupta, S. K., Madan, S., & Tewari, U. B. (1995). The class l(log l)α and some lacunary sets.

*Journal of the Australian Mathematical Society*,*58*(3), 387-403. https://doi.org/10.1017/S1446788700038374