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Eigenfunctions of the Laplace operator Eigenfunctions of the Laplace operator
| Content Provider | Semantic Scholar |
|---|---|
| Author | Laude, Emanuel |
| Copyright Year | 2014 |
| Abstract | The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces, that are required are introduced beforehand. In order to motivate the study of the Laplace eigenvalue problem, the connection between the Laplace eigenvalues and the geometry of the domain, to which the operator is applied, is demonstrated by presenting Weyl’s law. Furthermore it is shown how the Fourier transform can be derived from the consequences of the spectral theorem and orthogonal basis functions of the L space. Finally some applications of the Laplace eigenfunctions in 3D shape analysis are demonstrated briefly. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://vision.cs.tum.edu/_media/teaching/ss2014/seminar_shape_analysis/lb1_report.pdf |
| Alternate Webpage(s) | http://vision.in.tum.de/_media/teaching/ss2014/seminar_shape_analysis/lb1_report.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
