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Orthogonal basis for spherical monogenics by step two branching

Roman Lávička, Vladimir Souček and Peter Van Lancker UGent (2012) ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. 41(2). p.161-186
abstract
Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R(m). They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on Rm. Fix the direct sum R(m) = R(p) circle plus R(q). In this article, we will study the decomposition of the space M(n)(R(m), C(m)) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result, we obtain a Spin(p) x Spin(q)- invariant orthonormal basis for M(n)(R(m), C(m)). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M(n)(R(m), C(m)).
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Branching rules, Clifford analysis, Spin groups, Dirac operators, Representations
journal title
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
Ann. Glob. Anal. Geom.
volume
41
issue
2
pages
161 - 186
Web of Science type
Article
Web of Science id
000299294500003
JCR category
MATHEMATICS
JCR impact factor
0.887 (2012)
JCR rank
51/296 (2012)
JCR quartile
1 (2012)
ISSN
0232-704X
DOI
10.1007/s10455-011-9276-y
language
English
UGent publication?
no
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2154824
handle
http://hdl.handle.net/1854/LU-2154824
date created
2012-06-15 11:24:17
date last changed
2016-12-19 15:44:35
@article{2154824,
  abstract     = {Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R(m). They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on Rm. Fix the direct sum R(m) = R(p) circle plus R(q). In this article, we will study the decomposition of the space M(n)(R(m), C(m)) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result, we obtain a Spin(p) x Spin(q)- invariant orthonormal basis for M(n)(R(m), C(m)). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M(n)(R(m), C(m)).},
  author       = {L{\'a}vi\v{c}ka, Roman and Sou\v{c}ek, Vladimir and Van Lancker, Peter},
  issn         = {0232-704X},
  journal      = {ANNALS OF GLOBAL ANALYSIS AND GEOMETRY},
  keyword      = {Branching rules,Clifford analysis,Spin groups,Dirac operators,Representations},
  language     = {eng},
  number       = {2},
  pages        = {161--186},
  title        = {Orthogonal basis for spherical monogenics by step two branching},
  url          = {http://dx.doi.org/10.1007/s10455-011-9276-y},
  volume       = {41},
  year         = {2012},
}

Chicago
Lávička, Roman, Vladimir Souček, and Peter Van Lancker. 2012. “Orthogonal Basis for Spherical Monogenics by Step Two Branching.” Annals of Global Analysis and Geometry 41 (2): 161–186.
APA
Lávička, R., Souček, V., & Van Lancker, P. (2012). Orthogonal basis for spherical monogenics by step two branching. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 41(2), 161–186.
Vancouver
1.
Lávička R, Souček V, Van Lancker P. Orthogonal basis for spherical monogenics by step two branching. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. 2012;41(2):161–86.
MLA
Lávička, Roman, Vladimir Souček, and Peter Van Lancker. “Orthogonal Basis for Spherical Monogenics by Step Two Branching.” ANNALS OF GLOBAL ANALYSIS AND GEOMETRY 41.2 (2012): 161–186. Print.