Invariant polynomials in harmonic analysis

Simple item page
dc.contributor.advisorSpyridon, Dendrinos
dc.contributor.advisorMustata, Andrei
dc.contributor.authorMurphy, Fergalen
dc.contributor.funderUniversity College Cork
dc.contributor.funderLa Trobe University
dc.date.accessioned2025-02-05T10:03:53Z
dc.date.available2025-02-05T10:03:53Z
dc.date.issued2024
dc.date.submitted2024
dc.description.abstractThis thesis presents a methodology for analysing equiaffine invariant measures on surfaces, building on a modified version of a comparability lemma from a 2019 work of P. Gressman. The research focuses on simplifying the process of calculating the equiaffine invariant measure for 2-surfaces in R^n by avoiding the need for a complete set of generators for the algebra of invariant polynomials. Instead, we compute a sufficient set of invariant polynomials whose intersection characterises the set of unstable points under the SL_2(C) action. Our approach is demonstrated on specific surfaces in R^6, R^10, and R^15, where we successfully identify the relevant invariant polynomials and use them, along with the modified lemma, to derive the associated density functions. These density functions can then be used to define the equiaffine invariant measure. The results offer a practical framework for understanding affine invariants in geometric contexts and suggest possible extensions to higher-dimensional surfaces and different group actions. This work aims to provide a foundation for future studies in geometric invariant theory and harmonic analysis, exploring the interplay between algebraic geometry, invariant theory, and analysis.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMurphy, F. M. 2024. Invariant polynomials in harmonic analysis. MSc Thesis, University College Cork.
dc.identifier.endpage68
dc.identifier.urihttps://hdl.handle.net/10468/16966
dc.language.isoenen
dc.publisherUniversity College Corken
dc.relation.projectUniversity College Cork (School of Mathematical Sciences, Boole Fellowship)
dc.relation.projectLa Trobe University (School of Computing, Engineering and Mathematical Sciences)
dc.rights© 2024, Fergal Murphy.
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectHarmonic analysis
dc.subjectAlgebraic geometry
dc.subjectGeometric invariant theory
dc.subjectEquiaffine invariant measure
dc.titleInvariant polynomials in harmonic analysis
dc.typeMasters thesis (Research)en
dc.type.qualificationlevelMastersen
dc.type.qualificationnameMSc - Master of Scienceen
Files
Original bundle
Now showing 1 - 2 of 2
Thumbnail Image
Name:
MurphyF_MRes2024.pdf
Size:
671.63 KB
Format:
Adobe Portable Document Format
Description:
Full Text E-thesis
Download
Thumbnail Image
Name:
MurphyF_MRes2024_Submission for examination form.pdf
Size:
567.28 KB
Format:
Adobe Portable Document Format
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
5.2 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Research Theses
College of Science, Engineering and Food Science - Masters by Research Theses
Mathematical Sciences - Masters by Research Theses