Category:Orthonormal Sets

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This category contains results about Orthonormal Sets.
Definitions specific to this category can be found in Definitions/Orthonormal Sets.


Let $I$ be an indexing set.

Let $S := \family {\map {\phi_i} x}_{i \mathop \in I}$ be an indexed family of real functions all of which are integrable over the interval $\openint a b$.


Let $S$ have the property that:

$\forall m, n \in I: \displaystyle \int_a^b \map {\phi_m} x \map {\phi_n} x \rd x = \delta_{m n}$

where $\delta_{m n}$ denotes the Kronecker delta.


Then $S$ is defined as orthonormal.