# Set of Functions on Circle forms Vector Space

Jump to navigation
Jump to search

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: Not sure what happened here...If you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

the set of functions $\map f \phi$ on the circle (0 \le \phi < 2 \pi) forms a vector space:

- $\ds \map f \phi = \sum_{m \mathop = -\infty}^{+\infty} a_m e^{i m \phi}$

for integer m

- 1974: Robert Gilmore:
*Lie Groups, Lie Algebras and Some of their Applications*... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $4$. LINEAR VECTOR SPACE: Example $4$