A pseudo-differential calculus on graded nilpotent Lie groups

Véronique Fischer, Michael Ruzhansky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

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 languageEnglish
Title of host publicationFourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
EditorsM. V. Ruzhansky, V. Turunen
PublisherSpringer International Publishing
Pages107-132
Number of pages26
ISBN (Print)9783319025490
Publication statusPublished - 1 Jan 2014
EventInternational Conference on Fourier Analysis and Pseudo-Differential Operators, 2012 - Helsinki, Finland
Duration: 25 Jun 201229 Jun 2012

Publication series

NameTrends in Mathematics
Volume63

Conference

ConferenceInternational Conference on Fourier Analysis and Pseudo-Differential Operators, 2012
CountryFinland
CityHelsinki
Period25/06/1229/06/12

Fingerprint

Nilpotent Lie Group
Differential Calculus
Difference Operator
Operator
Representation Theory
Quantization
Calculus
Algebra
Class

Keywords

  • Nilpotent Lie groups
  • Pseudo-differential operators

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fischer, V., & Ruzhansky, M. (2014). A pseudo-differential calculus on graded nilpotent Lie groups. In M. V. Ruzhansky, & V. Turunen (Eds.), 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.

Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations. ed. / M. V. Ruzhansky; V. Turunen. Springer International Publishing, 2014. p. 107-132 (Trends in Mathematics; Vol. 63).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fischer, V & Ruzhansky, M 2014, A pseudo-differential calculus on graded nilpotent Lie groups. in MV Ruzhansky & V Turunen (eds), 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.
Fischer V, Ruzhansky M. A pseudo-differential calculus on graded nilpotent Lie groups. In Ruzhansky MV, Turunen V, editors, Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations. Springer International Publishing. 2014. p. 107-132. (Trends in Mathematics).
Fischer, Véronique ; Ruzhansky, Michael. / A pseudo-differential calculus on graded nilpotent Lie groups. Fourier Analysis - Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations. editor / M. V. Ruzhansky ; V. Turunen. Springer International Publishing, 2014. pp. 107-132 (Trends in Mathematics).
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