Solvability of invariant sublaplacians on spheres and group contractions

Fulvio Ricci; Jérémie Unterberger

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2001)

  • Volume: 12, Issue: 1, page 27-42
  • ISSN: 1120-6330

Abstract

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In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians L α on the spheres S 2 ⁢ n + 1 ≃ U ⁢ n + 1 / U ⁢ n . In the second part, we introduce a larger family of left-invariant sublaplacians L α , β on S 3 ≃ S ⁢ U ⁢ 2 and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.

How to cite

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Ricci, Fulvio, and Unterberger, Jérémie. "Solvability of invariant sublaplacians on spheres and group contractions." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.1 (2001): 27-42. <http://eudml.org/doc/252417>.

@article{Ricci2001,
abstract = {In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians $\mathcal\{L\}_\{\alpha\}$ on the spheres $S^\{2n+1\} \simeq U(n+1)/U(n)$. In the second part, we introduce a larger family of left-invariant sublaplacians $\mathcal\{L\}_\{\alpha,\beta\}$ on $S^\{3\} \simeq SU(2)$ and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.},
author = {Ricci, Fulvio, Unterberger, Jérémie},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Local solvability; Hypoellipticity; Invariant differential operators; Lie group contractions; local solvability; hypoellipticity; invariant differential operators},
language = {eng},
month = {3},
number = {1},
pages = {27-42},
publisher = {Accademia Nazionale dei Lincei},
title = {Solvability of invariant sublaplacians on spheres and group contractions},
url = {http://eudml.org/doc/252417},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Ricci, Fulvio
AU - Unterberger, Jérémie
TI - Solvability of invariant sublaplacians on spheres and group contractions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/3//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 1
SP - 27
EP - 42
AB - In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians $\mathcal{L}_{\alpha}$ on the spheres $S^{2n+1} \simeq U(n+1)/U(n)$. In the second part, we introduce a larger family of left-invariant sublaplacians $\mathcal{L}_{\alpha,\beta}$ on $S^{3} \simeq SU(2)$ and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
LA - eng
KW - Local solvability; Hypoellipticity; Invariant differential operators; Lie group contractions; local solvability; hypoellipticity; invariant differential operators
UR - http://eudml.org/doc/252417
ER -

References

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  7. Ricci, F., A Contraction of S ⁢ U ⁢ 2 to the Heisenberg group. Mh. Mat., 101, 1986, 211-225. Zbl0588.43007MR847376DOI10.1007/BF01301660
  8. Stein, E.M., Harmonic analysis. Princeton University Press, 1983. Zbl0821.42001
  9. Taylor, M.E., Noncommutative harmonic analysis. AMS, Mathematical surveys and monographs, 1986. Zbl0604.43001MR852988
  10. Ja, N. - Klimyk, A. U., Representation of Lie Groups and Special Functions. Vol. 2, Kluwer Academic Publishers, 1993. Zbl0809.22001MR1220225

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