Alshammari, Bandar Saad2019-11-142019-11-142019-12-01http://hdl.handle.net/2097/40245An overview on nonlocal Laplace operators acting on real-valued one-dimensional functions is presented. We provide a definition for nonlocal Laplace operators and present some basic examples. In addition, we show that, for vanishing nonlocality, the nonlocal Laplacian of a sufficiently differentiable one-dimensional function approaches the second derivative of the function. Moreover, we compute the Fourier multipliers of the nonlocal Laplacian and show that these multipliers converge to the multipliers of the Laplacian in the limit of vanishing nonlocality. Furthermore, we consider a nonlocal diffusion equation and provide an integral representation for its solution in terms of the Fourier multipliers of the nonlocal Laplacian.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Nonlocal LaplacianFourier multipliersReport