It says that the only functions killed by are constant functions.

This is multiplied by K which could be a constant or a function of frequency.

The rule holds in that case because the derivative of a constant function is 0.

The identity element comes from a constant function which is non-zero.

Let denote the space of locally constant functions on with compact support.

As mentioned above, every constant function is its own Weierstrass transform.

However, the symmetry group of constant functions is G itself.

The constant ranking function assigning the same score to all documents.

A constant function is a trivial example of a step function.

For example, the derivative of a constant function is zero.