For example, one may ask the question of meaningfully interpreting:formula_2as a square root of the differentiation operator (an operator half iterate), i.e., an expression for some operator that when applied "twice" to a function will have the same effect as differentiation.
For example, one may ask the question of meaningfully interpreting:formula_2as an analog of the functional square root for the differentiation operator (an operator half iterated), i.e., an expression for some linear operator that when applied "twice" to any function will have the same effect as differentiation.