Definition:Real-Valued Periodic Function Space
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Definition
Let $I = \closedint 0 T$ be a closed real interval.
Let $\map C I$ be the space of real-valued functions, continuous on $I$.
Let the elements of $\map C I$ be real periodic functions with the period $T$:
- $f \in \map C I: \map f T = \map f 0$
Then the set of all such mappings $f$ is known as real-valued periodic (over $I$) function space and is denoted by $\map {C_{per}} I$:
- $\map {C_{per}} I:= C_{per} \paren {I, \R} = \set {f : I \to \R : \map f T = \map f 0}$
Sources
- 2013: Philippe G. Ciarlet: Linear and Nonlinear Functional Analysis with Applications: Main Notations