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
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