# Real Analysis : Hilbert Space, Inner Product and Maps

Let V=L2[-1,1] be the Hilbert space of functions over the time interval [-1,1] with inner

product

......

Let P 5 V be the subspace of polynomials of order 4 or less, endowed with the inner

product and norm of V, and let

.....

be its natural basis. Define a

linear transformation S as

......

Show that the subspace P 5 is invariant under S. That is, verify that S maps members of P 5

back into P 5 . Define T as the restriction of S to P 5 .

https://brainmass.com/math/real-analysis/151410

#### Solution Summary

Hilbert Space, Inner Product and Maps are investigated.

$2.19