Finite and infinite decomposition.
If f is smooth then the relationship to Harmonic Analysis.
Groups of symmetries: the circle group, the additive group and the Pontryagin dual of the circle group.
Relationship to partial differential equations.
Finite and infinite decomposition.
If f is smooth then the relationship to Harmonic Analysis.
Groups of symmetries: the circle group, the additive group and the Pontryagin dual of the circle group.
Relationship to partial differential equations.
Relationship to even and odd functions.
Decomposing generic functions into a superposition of symmetric functions.
Decomposition into harmonics.