### Abstract

We examine distributions on T^{1}= R/ (2 πZ) whose Fourier coefficients are of the form (log n) ^{- 1}, and variants. These distributions are smooth except at θ= 0 , and the nature of their singularities at θ= 0 turns out to be much more complex than those of their counterparts that involve positive powers of log n. We also study related Fourier transforms. We move from one dimension to higher dimensions, where a wider variety of phenomena arise, and more subtle analytical techniques are called for.

Language | English (US) |
---|---|

Pages | 780-829 |

Number of pages | 50 |

Journal | Journal of Fourier Analysis and Applications |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2018 |

### Fingerprint

### Keywords

- Asymptotics
- Conormal distribution
- Fourier series
- Fourier transform
- Pseudodifferential operator
- Symbols

### ASJC Scopus subject areas

- Analysis
- Mathematics(all)
- Applied Mathematics

### Cite this

**Asymptotics for Some Non-classical Conormal Distributions Whose Symbols Contain Negative Powers of log | ξ|.** / Taylor, Michael.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Asymptotics for Some Non-classical Conormal Distributions Whose Symbols Contain Negative Powers of log | ξ|

AU - Taylor,Michael

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We examine distributions on T1= R/ (2 πZ) whose Fourier coefficients are of the form (log n) - 1, and variants. These distributions are smooth except at θ= 0 , and the nature of their singularities at θ= 0 turns out to be much more complex than those of their counterparts that involve positive powers of log n. We also study related Fourier transforms. We move from one dimension to higher dimensions, where a wider variety of phenomena arise, and more subtle analytical techniques are called for.

AB - We examine distributions on T1= R/ (2 πZ) whose Fourier coefficients are of the form (log n) - 1, and variants. These distributions are smooth except at θ= 0 , and the nature of their singularities at θ= 0 turns out to be much more complex than those of their counterparts that involve positive powers of log n. We also study related Fourier transforms. We move from one dimension to higher dimensions, where a wider variety of phenomena arise, and more subtle analytical techniques are called for.

KW - Asymptotics

KW - Conormal distribution

KW - Fourier series

KW - Fourier transform

KW - Pseudodifferential operator

KW - Symbols

UR - http://www.scopus.com/inward/record.url?scp=85015644103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015644103&partnerID=8YFLogxK

U2 - 10.1007/s00041-017-9537-7

DO - 10.1007/s00041-017-9537-7

M3 - Article

VL - 24

SP - 780

EP - 829

JO - Journal of Fourier Analysis and Applications

T2 - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 3

ER -