In this exercise, the indicated function norms are taken over all of R. a. ||fn|| = 1. but ||fn||2 as n

In this exercise, the indicated function norms are taken over all of R.
a.

||fn|| = 1. but ||fn||2 †’ ˆž as n †’ ˆž
(b) Explain why there is no constant C such that ||f||2 ‰¤ C || f ||ˆž for all functions f.
(c)

that || f || = 1. but ||fn||ˆž as n †’ 00. Conclude that there is no constant C such that ||f||ˆž (d) Construct similar examples that disprove the related inequalities
(i) ||f||ˆž ‰¤ C ll/H,
(ii) ||f||. ‰¤ C||f||2
(iii) || f || ‰¤ C || f ||,

Prove that Let Iotherwise. Let f,(x) V 2. 0 otherwise. n-.-n, Prove =