Multiplicative system
From Encyclopedia of Mathematics
An orthonormal system of functions 
on 
satisfying the conditions:
1) for any two functions 
and 
the system 
contains their product 
;
2) for each function 
the system 
contains the function 
.
Examples of multiplicative systems are the exponential system 
, which is orthogonal on 
, and the Walsh system of functions.
References
| [1] | S. Kaczmarz, H. Steinhaus, "Theorie der Orthogonalreihen" , Chelsea, reprint (1951) |
| [2] | H.F. Harmuth, "Transmission of information by orthogonal functions" , Springer (1972) |
| [3] | R.W. Zeek (ed.) A.E. Showalter (ed.) , Applications of Walsh functions (Proc. Symp. Washington, April 1971) , Univ. Maryland (1971) |
How to Cite This Entry:
Multiplicative system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiplicative_system&oldid=33019
Multiplicative system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiplicative_system&oldid=33019
This article was adapted from an original article by A.V. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article