### Abstract

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantization given by the representation theory. They form an algebra of operators which shares many properties with the usual Hörmander calculus.

Original language | English |
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Title of host publication | Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations |

Editors | M. V. Ruzhansky, V. Turunen |

Publisher | Springer International Publishing |

Pages | 107-132 |

Number of pages | 26 |

ISBN (Print) | 9783319025490 |

Publication status | Published - 1 Jan 2014 |

Event | International Conference on Fourier Analysis and Pseudo-Differential Operators, 2012 - Helsinki, Finland Duration: 25 Jun 2012 → 29 Jun 2012 |

### Publication series

Name | Trends in Mathematics |
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Volume | 63 |

### Conference

Conference | International Conference on Fourier Analysis and Pseudo-Differential Operators, 2012 |
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Country | Finland |

City | Helsinki |

Period | 25/06/12 → 29/06/12 |

### Fingerprint

### Keywords

- Nilpotent Lie groups
- Pseudo-differential operators

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations*(pp. 107-132). (Trends in Mathematics; Vol. 63). Springer International Publishing.

**A pseudo-differential calculus on graded nilpotent Lie groups.** / Fischer, Véronique; Ruzhansky, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations.*Trends in Mathematics, vol. 63, Springer International Publishing, pp. 107-132, International Conference on Fourier Analysis and Pseudo-Differential Operators, 2012, Helsinki, Finland, 25/06/12.

}

TY - GEN

T1 - A pseudo-differential calculus on graded nilpotent Lie groups

AU - Fischer, Véronique

AU - Ruzhansky, Michael

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantization given by the representation theory. They form an algebra of operators which shares many properties with the usual Hörmander calculus.

AB - In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantization given by the representation theory. They form an algebra of operators which shares many properties with the usual Hörmander calculus.

KW - Nilpotent Lie groups

KW - Pseudo-differential operators

UR - http://www.scopus.com/inward/record.url?scp=84894238095&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783319025490

T3 - Trends in Mathematics

SP - 107

EP - 132

BT - Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations

A2 - Ruzhansky, M. V.

A2 - Turunen, V.

PB - Springer International Publishing

ER -