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Diffstat (limited to 'Fourier Series.page')
| -rw-r--r-- | Fourier Series.page | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index 56eb762..5704fd1 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -91,9 +91,9 @@ 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 $2n+1$-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'.(*perhaps someone can clarify this?*) -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: +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: ---> define inner product here |