Results 11 to 20 of about 1,215,177 (342)

Optimal codomains for the Laplace operator and the product Laplace operator

Journal of Function Spaces and Applications, 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.
Josefina Alvarez, Lloyd Edgar S. Moyo
doaj   +3 more sources

The standard Laplace operator [PDF]

manuscripta mathematica, 2017
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 ...
U. Semmelmann, G. Weingart
semanticscholar   +5 more sources

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, A. Katok, D. Bao, D. Bao, D. Bao, D. Burago, D. Egloff, D. Egloff, D. Sullivan, E. B. Davies, F. Ledrappier, H. Akbar-Zadeh, H.-B. Rademacher, I. Chavel, I. Chavel, J. Hersch, M. Anastasiei, M. Berger, M. Crampon, M. Reed, M. Reed, M. Reed, M. T. Anderson, P. Centore, P. Centore, P. Foulon, P. Foulon, P. Foulon, P. H. Bérard, P. L. Antonelli, R. D. Holmes, R. L. Bryant, R. L. Bryant, R. L. Bryant, R. Narasimhan, S. Gallot, T. Kato, Thomas Barthelmé, V. Bangert, W. Ziller, Z. Shen   +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, Ivanov, Sergei, Kurylev, Yaroslav   +2 more
core   +6 more sources

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, Oste, Roy, Van der Jeugt, Joris   +2 more
core   +5 more sources

Laplace operators on holomorphic Lie algebroids [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid.
Ionescu Alexandru
doaj   +4 more sources

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.
H. M. Khudaverdian, H. M. Khudaverdian, Theodore Voronov   +2 more
openalex   +5 more sources

On the fractional Laplace-Bessel operator

AIMS Mathematics
In this paper, we propose a novel approach to the fractional power of the Laplace-Bessel operator $ \Delta_{\nu} $, defined as$ \Delta_{\nu} = \sum\limits_{i = 1}^{n}\frac{\partial^2}{\partial x_{i}^2} + \frac{\nu_i}{x_{i}}\frac{\partial}{\partial x_{i}}
Borhen Halouani, Fethi Bouzeffour
doaj   +2 more sources

Laplace Operator and Polynomial Invariants

Journal of Algebra, 1998
AbstractLetAbe a finite dimensional simple algebra (not necessarily associative) over the field of complex numbersC, and letGdenote the automorphism group Aut(A). Suppose thatAhas a symmetric nondegenerate associativeG-invariant bilinear form 〈x,y〉 and a compact real form, i.e., a subalgebraBoverRof dimension dimRB=dimCA, whereAis equal to the span ...
A.V. Iltyakov
openalex   +3 more sources

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
openaire   +3 more sources