If for a function space , we can define the scalar product of any given 2 functions as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{a}^{b}dx f^{*}(x)g(x) [/tex]

what happens with its analogue the 'dot/cross' (vectorial product of 2 vectors which is itself another vector orthogonal to the 2 given ones)

the question is not in vane since to define the dual basis of any vector

[tex] \tilde{\omega}^i = {1 \over 2} \, \left\langle { \epsilon^{ijk} \, (\vec e_j \times \vec e_k) \over \vec e_1 \cdot \vec e_2 \times \vec e_3} , \qquad \right\rangle [/tex]

hence for a function space we would find that.

[tex] h(x) = (??) f(x) \times g(x) [/tex]

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# Infinite dimensional vectorial (dot) product)

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