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Products of operators

The result of an operation on a function is another function, therefore we can naturally apply an operator on another operator. In other words, if $ L_1$ , $ L_2$ are two operators, then we can define $ L_1L_2$ as $ L_1L_2[x] = L_1[L_2[x]]$ , provided that $ L_1[L_2[x]]$ makes sense mathematically. This is called the composition of the operators $ L_1$ and $ L_2$ . Because in the discrete case the composition of operators is in fact the multiplication $ L_1L_2$ of the two matrices $ L_1$ , $ L_2$ the operator composition is usually referred to as operator product and denoted by $ L_1L_2$ is used. The composition of operators can be naturally extended to any finite product $ L_1\cdots L_{n-1}L_n$ . The product of up to 3 operators is implemented in [sec:chain]chain.c.