Theorems in functional analysis

Lauricella's theorem

In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely: Theorem. A necessary and sufficient condition that a normal orthogonal set be closed is that the formal series for each function of a known closed normal orthogonal set in terms of converge in the mean to that function. The theorem was proved by Giuseppe Lauricella in 1912. (Wikipedia).

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Related pages

Orthogonal functions | Convergence of random variables