# Exterior product in L^2 space

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?

• – Henricus V. Feb 20 '16 at 5:12
• 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. – Mason Feb 20 '16 at 7:21
• Exterior product can be defined as asymmetric tensor products. – Henricus V. Feb 20 '16 at 15:11