Definition:Antiperiodic Function

Definition

Antiperiodic Real Function

Let $f: \R \to \R$ be a real function.

Then $f$ is anti-periodic if and only if:

$\exists L \in \R_{\ne 0}: \forall x \in \R: -f \left({x}\right) = f \left({x + L}\right)$

Antiperiodic Complex Function

Let $f: \C \to \C$ be a complex function.

Then $f$ is anti-periodic if and only if:

$\exists L \in \C_{\ne 0}: \forall x \in \C: -f \left({x}\right) = f \left({x + L}\right)$

Antiperiodic Element

Let $L \in X_{\ne 0}$.

Then $L$ is an anti-periodic element of $f$ if and only if:

$\forall x \in X: - \map f x = \map f {x + L}$

Antiperiod

The antiperiod of $f$ is the smallest value $\cmod L \in \R_{\ne 0}$ such that:

$\forall x \in X: - \map f x = \map f {x + L}$

where $\cmod L$ is the modulus of $L$.

Also see

• General Antiperiodicity Property

• Results about antiperiodic functions can be found here.