Skip to main content
Download book PDF
View expanded cover

Quantization on Nilpotent Lie Groups pp 171–269Cite as

Birkhäuser

Rockland operators and Sobolev spaces

  • 5524 Accesses

Part of the Progress in Mathematics book series (PM,volume 314)

Abstract

In this chapter, we study a special type of operators: the (homogeneous) Rockland operators. These operators can be viewed as a generalisation of sub-Laplacians to the non-stratified but still homogeneous (graded) setting. The terminology comes from a property conjectured by Rockland and eventually proved by Helffer and Nourrigat in [HN79], see Section 4.1.3.

Keywords

  • Sobolev Space
  • Heat Kernel
  • Functional Calculus
  • Fractional Power
  • Convolution Kernel

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Download chapter PDF

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bath, Bath, UK

    Veronique Fischer

  2. Department of Mathematics, Imperial College London, London, UK

    Michael Ruzhansky

Authors
  1. Veronique Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Ruzhansky
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

This chapter is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

Copyright information

© 2016 The Author(s)

About this chapter

Cite this chapter

Fischer, V., Ruzhansky, M. (2016). Rockland operators and Sobolev spaces. In: Quantization on Nilpotent Lie Groups. Progress in Mathematics, vol 314. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29558-9_4

Download citation