I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 3, PAGES 653-674
Approximation of -ary functions by
functions from the given system
A. S. Ambrosimov
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Problems of -ary functions
approximation by functions from the given system are investigated in
In particular, generalization of Golomb theorem is
obtained in the case of ring or finite field
The definition of -ary functions equivalency
with respect to the given functions system is introduced.
Classes of equivalency with respect to the linear functions system
over finite field or ring are described.
Limit theorems on cardinality of random -ary functions equivalency
class are proved.
Also in this paper we found functions which minimize maximum
probability of coincidence with linear functions in one variable over
finite ring with identity.
All articles are
published in Russian.
Last modified: January 20, 2000