Manuscript VII-H@1 · VII-H.tex · section · d20d2a9f

A logarithmic reference prescription

An explicit extension and the full normalization class › A logarithmic reference prescription · lines 782–807

VII-H@1#eq:log-function, VII-H@1#eq:reference-response

For $μ > 0$ , let

L_{μ} (z) = {lo g (μ^{2} s (z)), 0, t > 0, s (z) > 0, otherwise .

This is a locally integrable function. Its definition is not a product of an undefined distribution with a characteristic function.

Define

R_{μ} = \frac{ℏ}{64 π ^{3}} □^{2} L_{μ} .

The square denotes two applications of $□$ , hence four derivatives in total.

Displayed formulas in this passage

VII-H@1#eq:log-function · line 785
$L_{μ} (z) = {lo g (μ^{2} s (z)), 0, t > 0, s (z) > 0, otherwise .$
VII-H@1#eq:reference-response · line 798
$R_{μ} = \frac{ℏ}{64 π ^{3}} □^{2} L_{μ} .$