题目：Hermitian derivatives, spline functions and the discrete biharmonic operator
时间：11月1日上午9:10 － 10:10
摘要: The strong connection between cubic spine functions (on an interval) and the biharmonic operator is studied. It is shown in particular that the (scaled) fourth-order distributional derivative of the cubic spline is identical to the compact discrete biharmonic operator. The latter is constructed in terms of the discrete Hermitian derivative. There is no maximum principle for the fourth-order equation. However, a positivity result is derived, both for the continuous and the discrete biharmonic equation. A remarkable fact is that the kernel of the discrete operator is (up to scaling) equal to the grid evaluation of the continuous kernel. Explicit expressions are presented for both kernels. The relation between the (infinite) set of eigenvalues of the fourth-order Sturm-Liouville problem and the finite set of eigenvalues of the discrete biharmonic operator is studied. It is well known that in general eigenvalues of finite-dimensional approximating operators do not converge to the eigenvalues of the full operator. However, we show that here it is true.
报告人简介：Matania Ben-Artzi is a Professor at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, Israel. He has held visiting positions in various universities and research institutes in Sweden, USA, Brazil, Italy, France, Canada, England, and China. His primal research interests include: Spectral and Scattering Theory of Linear Operators, Navier-Stokes equations, Hamilton-Jacobi equations, Nonlinear Hyperbolic Conservation Laws, and Computational Fluid Dynamics. Professor Ben-Artzi has published 3 books and around 100 research articles.