Sum Rule Functions

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Abstract
In many cases the quantum mechanical sum rules S(k), as k ranges over all real values such that S(k) is convergent, form a particular example from a class of functions called sum rule functions. If a set of up to five values taken by a sum rule function is given, then, by the use of another class of functions called N‐sum rule functions, it is shown how one can impose the very best possible bounds on the sum rule function for arbitrary k, on the basis of the given information. In particular, these results apply to quantum mechanical sum rules.

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