Let V denote the vectore space of continuously differentiable functions, ƒ, over the interval [0,1] such that ƒ(0)=0.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose Φ is-contained C∞ [0,1] (set of infinitely differentiable functions over the interval [0,1]) and define the operator

TΦ:V→R:ƒ→∫ƒ'(x)Φ(x)dx 0,1

Describe the null space of TΦ if Φ = x (Hint: integration by parts)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Describe this null space!

**Physics Forums | Science Articles, Homework Help, Discussion**