nLab periodic function

Contents

Contents

Definition

A periodic function on a \mathbb{Z}-module MM with a strict linear order <\lt where left and right addition are strictly monotonic is a function f:MMf:M \to M with a positive element aMa \in M, 0<a0 \lt a called the period, such that for all integers nn \in \mathbb{Z} and elements xMx \in M, f(x)=f(x+na)f(x) = f(x + n a), and for any other integer bMb \in M where 0<b0 \lt b and for all integers nn \in \mathbb{Z} and elements xMx \in M, f(x)=f(x+nb)f(x) = f(x + n b), aba \leq b.

See also

References

See also:

Created on May 16, 2022 at 17:37:58. See the history of this page for a list of all contributions to it.