Bandar Alshammari, Kansas State University
Major Professor, Dr. Bacim Alali, Kansas State University
Title: A Nonlocal Laplacian in One Dimension
Abstract: In this report, we provide an overview on nonlocal Laplace operators acting on real-valued one-dimensional functions. In Chapter 1, we define a nonlocal Laplacian and present some basic examples. In addition, we show a connection between the nonlocal Laplacian in one-dimension and the second derivative. In Chapter 2, we review some basic properties of the Fourier transform and provide examples. In Chapter 3, we present the Fourier multipliers for the nonlocal Laplacian and show that these multipliers converge to the multipliers of the Laplacian in the limit of vanishing nonlocality.
Tuesday, November 12 at 1:00pm