ABSTRACT
The inner product was defined by equation (98); here, a=0 and b=1. Note that these functions do not have to be continuous. This is a Hilbert space that is usually denoted L2[0, 1]. The restriction to functions defined on [0, 1] is not a real limitation
for physical problems, where we can never measurements over an infinite time or space interval. If a function g(x) is defined on the interval [a, b], where b>a, then making the substitution (x-a)/(b-a)? x produces a new function defined on [0, 1].
