Cambridge University Press, Cambridge (1997) Rosenberg, S.: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds, 2nd edn. Urakawa, H.: Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian, 2nd edn. 83, 992–997 (2015)īiyikoglu, T., Leydold, J., Stadler, P.F.: Laplacian Eigenvectors of Graphs, 1st edn. Styer, D.F.: The geometrical significance of the Laplacian. Keywordsįiedler, M.: Geometry of the Laplacian. And we will investigate the properties of this kind of representation in parallelisms to standard well-known versions. Also, we will introduce the formula for the Laplace operator in the space whose structure is determined by a fuzzy partition . In this article, we will mention some of the various ways in which this operator can be introduced in relation to the corresponding space. Our goal was to find such a representation, that would be simple for computations but at the same time applicable to more general domains, possibly to spaces without a notion of a classic distance. Therefore, we investigated this operator from point of view of spaces, where distance may not be explicitly defined and thus is being replaced by more general, so-called, proximity. a non-regular graph or even a manifold, but the Laplace operator is still closely bound to the space structure. There are cases when underlying space is considered to be e.g. However, signals, in general, can be defined not only on Euclidean domains such as regular grids (in case of images). in signal and image processing applications . This operator attracts a lot of attention e.g. It appears in many research areas and every such area defines it accordingly based on underlying domain and plans on follow-up applications. Laplace operator is a diverse concept throughout natural sciences.
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