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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1996 • Question 13

Question

Math 6410 • ODE Fall 1996 • Question 13

Let \(G\subset \mathbb {R}^N\) be an open set and let \(m\ge 0\) be an integer. Let \(f\in C^m(G)\) be real or complex valued function. Show that \(f\) may be identified with a distribution \(T_f\) and compute the distributional derivatives of \(T_f\) up to order \(m\).

Raw LaTeX

Let \(G\subset\R^N\) be an open set and let \(m\ge0\) be an integer. Let
\(f\in C^m(G)\) be real or complex valued function. Show that \(f\) may be identified
with a distribution \(T_f\) and compute the distributional derivatives of \(T_f\) up to
order \(m\).

Topic Tags

Distributions and Weak Solutions