Fundamental solutions for the two dimensional affine group and H<sup>n+1</sup>

Craddock, M

Fundamental solutions for the two dimensional affine group and H<sup>n+1</sup>

Craddock, M

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Publication Type:: Journal Article
Citation:: Journal of Mathematical Analysis and Applications, 2017, 445 (1), pp. 953 - 970
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Craddock, M	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	Journal of Mathematical Analysis and Applications, 2017, 445 (1), pp. 953 - 970	en_US
dc.identifier.issn	0022-247X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/124872
dc.description.abstract	© 2016 Elsevier Inc. We derive the wave and heat kernels on the ax+b group, as well as the fundamental solution of the group Laplacian. We make particular use of the Kontorovich–Lebedev transform and a recent result of the author to produce new expressions for these kernels. Our results easily extend to the hyperbolic space Hn+1 for any n and the explicit formulas are given in n dimensions.	en_US
dc.relation.ispartof	Journal of Mathematical Analysis and Applications	en_US
dc.relation.isbasedon	10.1016/j.jmaa.2016.08.027	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Fundamental solutions for the two dimensional affine group and H<sup>n+1</sup>	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	445	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	445	en_US

Abstract:

© 2016 Elsevier Inc. We derive the wave and heat kernels on the ax+b group, as well as the fundamental solution of the group Laplacian. We make particular use of the Kontorovich–Lebedev transform and a recent result of the author to produce new expressions for these kernels. Our results easily extend to the hyperbolic space Hn+1 for any n and the explicit formulas are given in n dimensions.

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http://hdl.handle.net/10453/124872