Let L be a constant coefficient operator that can be factorized as a product of constant coefficient operators
Then the solution space of contains the solution space of each . in orther words,
Let . Since the factors commute, we can move to the rightmost position so that . Hence, Þ . QED.
If , then L is said to annihilate u. Thus, Theorem 8.7 can be rephrased as follows. If a factor Aj of L annihilates u, then L annihilates u.