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In my analysis homework, I have this expression:

$$ (\cdot | \cdot): \quad C[a,b] \times C[a,b] \rightarrow \mathbb{K}, \; (f,g) \mapsto (f |g) := \int_a^b f(x) \overline{g(x)} \;dx $$

Any idea what $\overline{g(x)}$ stands for?

EDIT

$\mathbb{K}$ is either $\mathbb{R}$ or $\mathbb{C}$.

fpmoo
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1 Answers1

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It is complex conjugate.

If $z = a+ib$, then $\overline{z} = a-ib.$

Eff
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    It is a hermitian dot product (sesqulinear form), useful when $f$ or $g$ are complex valued. Furthermore, if you take $f=g$, it gives the integral of the square of the modulus. – Jean Marie Apr 22 '17 at 12:24