(a) Show that the set of all square-integrable functions is a vector space (refer to Section A.1 for the definition). The main point is to show that the sum of two square-integrable functions is itself square-integrable. Use Equation 3.7. Is the set of all normalized functions a vector space?
(b) Show that the integral in Equation 3.6 satisfies the conditions for an inner product (Section A.2).

Equation 3.6

Equation 3.7

Transcribed Image Text:

b =ff(x) *g(x) dx. (flg) = (3.6)