Complete system of functions
From Encyclopedia of Mathematics
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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: http://encyclopediaofmath.org/index.php?title=Complete_system_of_functions&oldid=12534
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