Results 1 to 10 of about 121,443 (210)
A natural Finsler--Laplace operator [PDF]
Israel Journal of Mathematics, 2012 We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections ...
A. Grigor’yan +40 more
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A graph discretization of the Laplace-Beltrami operator [PDF]
Journal of Spectral Theory, 2014 We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.Comment: 29 ...
Burago, Dmitri +2 more
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On the algebra of symmetries of Laplace and Dirac operators [PDF]
Letters in Mathematical Physics, 2018 We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators.
De Bie, Hendrik +2 more
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The standard Laplace operator [PDF]
manuscripta mathematica, 2018 The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds.
Uwe Semmelmann, Gregor Weingart
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Laplace invariants of differential operators [PDF]
Illinois Journal of Mathematics, 2021 We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential invariants of partial differential operators under gauge transformations and introduce a sufficient condition for a set of
David Hobby, Ekaterina Shemyakova
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On odd Laplace operators [PDF]
Letters in Mathematical Physics, 2002 We consider odd Laplace operators acting on densities of various weight on an odd Poisson (= Schouten) manifold $M$. We prove that the case of densities of weight 1/2 (half-densities) is distinguished by the existence of a unique odd Laplace operator depending only on a point of an ``orbit space'' of volume forms.
Theodore Voronov +2 more
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The Higher Spin Laplace Operator [PDF]
Potential Analysis, 2016 This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a generalisation of the Laplace operator to higher spin as well as a second order analogue of the Rarita-Schwinger ...
Hendrik De Bie +2 more
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Laplace and Dirac operators on graphs
Linear and Multilinear Algebra, 2022 Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac operators on graphs, and we investigate graph-theoretic versions of the Schr dinger and Dirac equation.
Beata Casiday +4 more
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The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps [PDF]
, 2018 We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a ...
Flegel, Franziska, Heida, Martin
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Optimal codomains for the Laplace operator and the product Laplace operator
Journal of Function Spaces, 2007 An optimal codomain for an operator P (∂) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P (∂)S = T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case ...
Lloyd Edgar S. Moyo, Josefina Alvarez
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