(a) Show that the set of all square-integrable functions is a vector space (refer to Section A. 1 for the definition). Hint: 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 Δ.2). | Numerade
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A function f(x) is square integrable on [a, b] if\int_a^b|f(x)... | Filo
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