[MauiWarrior]

I am afraid it is a bit over my head. Would you be able to point me to the source?

[peterhj]

Not the most explanatory sources but function spaces essentially are vector spaces:

https://en.wikipedia.org/wiki/Vector_space#Function_spaces

http://mathworld.wolfram.com/HilbertSpace.html

[mlevental]

https://www.youtube.com/watch?v=7ICYxBuS2iw looks like a pretty elementary introduction