I've been learning a bit about exterior algebra and I got to thinking about Fourier series and how each term in the series acts as a basis vector with an inner product between these vectors defined as the integral of the product of their functional representations.

Is there a way to define an exterior product for such a space? If such a product exists are there uses for it?

What does this product look like explicitly in the case of Fourier series?

  • $\begingroup$ See Topological tensor product. $\endgroup$ – Henricus V. Feb 20 '16 at 5:12
  • $\begingroup$ Forgive me if I'm mistaken, but is the exterior product not distinct from the tensor product? I'm talking about something like the wedge product but in Fourier space. $\endgroup$ – Mason Feb 20 '16 at 7:21
  • $\begingroup$ Exterior product can be defined as asymmetric tensor products. $\endgroup$ – Henricus V. Feb 20 '16 at 15:11

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