Eigenvalue decompositions of kernels & the hyperbolic brachistochrone equation

Morrison, Peter G.

Eigenvalue decompositions of kernels & the hyperbolic brachistochrone equation

Morrison, Peter G.

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Publication Type:: Thesis
Issue Date:: 2024

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Field	Value	Language
dc.contributor.author	Morrison, Peter G.
dc.date.accessioned	2025-12-15T04:12:10Z
dc.date.available	2025-12-15T04:12:10Z
dc.date.issued	2024
dc.identifier.uri	http://hdl.handle.net/10453/190937
dc.description	University of Technology Sydney. Faculty of Science.	en_US.UTF-8
dc.description.abstract	The thesis addresses the theory of the brachistochrone, the hyperbolic heat kernel and various problems in index integration, including Kontorovich-Lebedev, Mehler-Fock and Whittaker transforms, linking these special transforms to sets of eigenfunction solutions for various hyperbolic differential equations. Developing a concise theory from the perspective of time optimal quantum control and the quantum brachistochrone principle, this work shows the underlying linkages between theories of geometric algebra, group operators and the differential geometries on hyperbolic space. Particular emphasis is placed on special function theory and the Fubini-Study metric of different hyperbolic spaces. Application of index transforms to the projection-slice theorem is given, including Asian option pricing, & analysis of Radon and Weierstrass transformations.	en_US.UTF-8
dc.format	Thesis (PhD)
dc.language.iso	en_US	en_US.UTF-8
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/190937/1/thesis.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	© 2024 Peter G. Morrison
dc.rights	au.edu.uts.lib/cph
dc.title	Eigenvalue decompositions of kernels & the hyperbolic brachistochrone equation	en_US.UTF-8
dc.type	Thesis
utslib.copyright.status	open_access	*

Abstract:

The thesis addresses the theory of the brachistochrone, the hyperbolic heat kernel and various problems in index integration, including Kontorovich-Lebedev, Mehler-Fock and Whittaker transforms, linking these special transforms to sets of eigenfunction solutions for various hyperbolic differential equations. Developing a concise theory from the perspective of time optimal quantum control and the quantum brachistochrone principle, this work shows the underlying linkages between theories of geometric algebra, group operators and the differential geometries on hyperbolic space. Particular emphasis is placed on special function theory and the Fubini-Study metric of different hyperbolic spaces. Application of index transforms to the projection-slice theorem is given, including Asian option pricing, & analysis of Radon and Weierstrass transformations.

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http://hdl.handle.net/10453/190937