# Complete system of functions

From Encyclopedia of Mathematics

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: http://encyclopediaofmath.org/index.php?title=Complete_system_of_functions&oldid=12534

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article