### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Australian Mathematical Society*,

*58*(3), 387-403. https://doi.org/10.1017/S1446788700038374

**The class l(log l)α and some lacunary sets.** / Gupta, Sanjiv Kumar; Madan, Shobha; Tewari, U. B.

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 58, no. 3, pp. 387-403. https://doi.org/10.1017/S1446788700038374

}

TY - JOUR

T1 - The class l(log l)α and some lacunary sets

AU - Gupta, Sanjiv Kumar

AU - Madan, Shobha

AU - Tewari, U. B.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84976069211&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976069211&partnerID=8YFLogxK

U2 - 10.1017/S1446788700038374

DO - 10.1017/S1446788700038374

M3 - Article

VL - 58

SP - 387

EP - 403

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 3

ER -