Klassifikation av polygoner med trigonometriska egenfunktioner till Laplaceoperatorn under Dirichletrandvillkor

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dc.contributor.authorNordell, Henrik
dc.contributor.authorThim, Oliver
dc.contributor.authorBlom, Max
dc.contributor.authorVahnberg, Jack
dc.contributor.departmentChalmers tekniska högskola / Institutionen för matematiska vetenskapersv
dc.contributor.departmentChalmers University of Technology / Department of Mathematical Sciencesen
dc.date.accessioned2019-07-05T12:03:04Z
dc.date.available2019-07-05T12:03:04Z
dc.date.issued2019
dc.description.abstractWe consider the eigenstructure of the Laplace operator on triangles with the angles (60°, 60°,60°); (30°, 60°,90°) och (45°, 45°,90°). Using the earlier work by M. Práger (1998) and M. A. Pinsky (1980) we find eigenfunctions of the Laplace operator with Dirichlet boundary conditions. We show completeness of eigenfunctions in L2 for each triangle. Moreover, we present a result by Brian J. McCartin (2008) that classifies which polygons have a complete set of trigonometric eigenfunctions. These polygons are the triangles mentioned above, the rectangle and the square. We connect McCartins result to symmetries of lattices, crystals and Weyl groups. In 1980 Pierre H. Bérard studied the connection between different types of eigenfunctions and symmetries and proved that all alcoves of Weyl groups have trigonometric eigenfunctions. We point out the fact that in R2 the converse is also true. That is, all polygons with a complete set of trigonometric eigenfunctions are alcoves.
dc.identifier.urihttps://hdl.handle.net/20.500.12380/257361
dc.language.isoswe
dc.setspec.uppsokPhysicsChemistryMaths
dc.subjectGrundläggande vetenskaper
dc.subjectMatematik
dc.subjectBasic Sciences
dc.subjectMathematics
dc.titleKlassifikation av polygoner med trigonometriska egenfunktioner till Laplaceoperatorn under Dirichletrandvillkor
dc.type.degreeExamensarbete för kandidatexamensv
dc.type.degreeBachelor Thesisen
dc.type.uppsokM2
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