Complete system of functions

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An orthonormal system of functions in some Hilbert space such that in there is no function orthogonal to all the functions in that family. A system of functions that is complete in one space may be incomplete in another. For example, the system

forms a complete system of functions in the space but does not form a complete system in the space .

How to Cite This Entry:
Complete system of functions. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article