Question

Let $\varphi$ be a distribution of order $n$, and let $h$ be in $T^n$. Define $h \varphi$, and prove that this distribution is of order $n$.

   Let $\varphi$ be a distribution of order $n$, and let $h$ be in $T^n$. Define $h \varphi$, and prove that this distribution is of order $n$.

Mathematical physics

Mathematical physics

Robert Geroch 1st Edition

Chapter 47, Problem 319

Instant Answer

Step 1

A distribution of order \( n \), denoted by \( \varphi \), is a continuous linear functional on the space of test functions \( C_c^\infty(\mathbb{R}^d) \) such that for any compact set \( K \subset \mathbb{R}^d \), there exists a constant \( C \) and a multi-index Show more…

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Let $\varphi$ be a distribution of order $n$, and let $h$ be in $T^n$. Define $h \varphi$, and prove that this distribution is of order $n$.

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