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.

Interesting scientific or quantitative thoughts or ideas!

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.