0

I am trying to understand periodic Lebesgue spaces $L^p(\mathbb{T})$.

In particular, I have trouble understanding how the scaling $[\delta_\lambda f](x) = f(\lambda x)$ and translation $[\tau_h f](x) = f(x+h)$ are defined.

What do I have to keep in mind when studying these two mappings on the torus?

It seems to be natural to me that for example $\| f \|_p = \| \tau_h f \|_p$ for all $h$. Is that true?

If you could share any insight or references with me that would bei highly appreciated.

Rooibos
  • 179
  • Related (see the first few lines in the question): https://math.stackexchange.com/questions/4316072/do-full-rank-matrices-in-mathbb-zd-times-d-preserve-integrals-of-functions – Calvin Khor May 08 '23 at 08:37

0 Answers0