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| -rw-r--r-- | Fourier Series.page | 2 |
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diff --git a/Fourier Series.page b/Fourier Series.page index 6e780a7..56eb762 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -91,7 +91,7 @@ f & = & \Sigma e^{inx}\\ $$ ##Definition of Inner Product of Functions -We begin proving this hypothesis by considering that any function on the right-hand side of our hypothesis is uniquely defined by the co-efficients of the terms a_0 through a_n and b_1 through b_n. This can be taken to mean that every function is really a vector in an n-dimensional Hilbert space. +We begin proving this hypothesis by considering that any function on the right-hand side of our hypothesis is uniquely defined by the co-efficients of the terms $a_0$ through $a_n$ and $b_1$ through $b_n$. This can be taken to mean that every function is really a vector in an $2n+1$-dimensional Hilbert space. We now proceed to define certain operations on these functions in Hilbert space. One operation that will be particularly useful is that of the inner product of two functions in Hilbert space: |