Linear Combination of Functions of Exponential Order
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Theorem
Let $f, g: \R \to \F$ be functions, where $\F \in \set {\R, \C}$.
Let $\lambda, \mu$ be complex numbers.
Suppose $f$ is of exponential order $a$ and $g$ is of exponential order $b$.
Then $\map {\paren {\lambda f + \mu g} } t = \lambda \, \map f t + \mu \, \map g t$ is of exponential order $\max \set {a, b}$.
Proof
Follows from:
$\blacksquare$