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A Note on Distal Functions
Author(s) -
FILALI M.
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb55892.x
Subject(s) - mathematics , generalization , character (mathematics) , combinatorics , group (periodic table) , function (biology) , polynomial , simple (philosophy) , pure mathematics , mathematical analysis , physics , geometry , biology , epistemology , quantum mechanics , philosophy , evolutionary biology
The function f(n) = exp( ip ( n )) is known to be distal on the group of the integers whenever p is a real polynomial. We establish a simple criterion from which we deduce the following generalization: Let R be a discrete ring, X a character of the additive group of R, and p a polynomial function on R and with coefficients in R . Then the function f ( s ) = X ( p ( s )) is distal on the additive group of R .