Rarita-Schwinger type operators on spheres and real projective space

Junxia Li; John Ryan; Carmen J. Vanegas

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 4, page 271-289
  • ISSN: 0044-8753

Abstract

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In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.

How to cite

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Li, Junxia, Ryan, John, and Vanegas, Carmen J.. "Rarita-Schwinger type operators on spheres and real projective space." Archivum Mathematicum 048.4 (2012): 271-289. <http://eudml.org/doc/251383>.

@article{Li2012,
abstract = {In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.},
author = {Li, Junxia, Ryan, John, Vanegas, Carmen J.},
journal = {Archivum Mathematicum},
keywords = {spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition; spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition},
language = {eng},
number = {4},
pages = {271-289},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Rarita-Schwinger type operators on spheres and real projective space},
url = {http://eudml.org/doc/251383},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Li, Junxia
AU - Ryan, John
AU - Vanegas, Carmen J.
TI - Rarita-Schwinger type operators on spheres and real projective space
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 4
SP - 271
EP - 289
AB - In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.
LA - eng
KW - spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition; spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition
UR - http://eudml.org/doc/251383
ER -

References

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  12. Ryan, J., Dirac operators on spheres and hyperbolae, Bol. Soc. Mat. Mexicana (3) 3 (2) (1997), 255–270. (1997) Zbl0894.30031MR1679305
  13. Van Lancker, P., Clifford Analysis on the Sphere, Clifford Algebra and their Application in Mathematical Physics (Aachen, 1996), Fund. Theories Phys., 94, Kluwer Acad. Publ., Dordrecht, 1998, pp. 201–215. (1998) Zbl0896.15015MR1627086
  14. Van Lancker, P., Higher Spin Fields on Smooth Domains, Clifford Analysis and Its Applications (Brackx, F., Chisholm, J. S. R., Souček, V., eds.), Kluwer, Dordrecht, 2001, pp. 389–398. (2001) Zbl1009.30029MR1890463
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