Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1997 • Question 9

Question

Math 6420 • PDE Fall 1997 • Question 9

Define and find the Green’s function for the discrete operator \(Lu=-\Delta u-\lambda u\) defined on the space of doubly infinite sequences \(u=\{u_n\}\), \(-\infty <n<\infty \), with \(\sum _{n=-\infty }^{\infty }u_n^2<\infty \), and with \((\Delta u)_n=u_{n+1}-2u_n+u_{n-1}\).

Raw LaTeX

Define and find the Green's function for the discrete operator
\(Lu=-\Delta u-\lambda u\) defined on the space of doubly infinite sequences
\(u=\{u_n\}\), \(-\infty<n<\infty\), with \(\sum_{n=-\infty}^{\infty}u_n^2<\infty\), and with
\((\Delta u)_n=u_{n+1}-2u_n+u_{n-1}\).

Topic Tags

Discrete Maximum Principles Distributions and Weak Solutions Fundamental Solutions Linear Programming and Optimization