Dispersion Relation
Any pair of equations giving the Real Part of a function as an integral of its Imaginary Part and theImaginary Part as an integral of its Real Part. Dispersion relationships imply causality in physics. Let
 | (1) |
 |  |  | (2) |
 | |  | (3) |
where
denotes the Cauchy Principal Value and 
and 
are Hilbert Transforms of each other. If the Complex function is symmetric such that 
, then | |  | (4) |
| |  | (5) |
- Alexander's Theorem
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