## Mathematics and Statistics Faculty Research & Creative Works

#### Title

A Class of I (1, 0)-sets

#### Abstract

A set E (L-HOOK) R, the real numbers, in an I(,0)-set if every bounded complex-valued function on E can be extended to an almost periodic function on R. Suppose (LAMDA) = {q(,j) : j=1,2,3,...} (L-HOOK) R('+) where q(,j+1)/q(,j) (GREATERTHEQ) q > 1 for all j. Let K = {k(,j) : j=1,2,3,...} be any subsequence of (LAMDA), and let {(LAMDA)(k(,j)) : j=1,2,3,...} be any sequence of disjoint subsets of (LAMDA). Define the blocked set^ (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)^ When K (INTERSECT) (LAMDA)(k(,j)) = (phi) for all j, E is called a restricted blocked set.^In this investigation it is shown that if q > 2, then any blocked set^formed from (LAMDA) is an I(,0)-set. Alternatively, if q > (1+SQRT.(5)/2 and(' )^inf{(VBAR)2 - q(,j+1)/q(,j))(VBAR) : j=1,2,3,...} > 0, then it is proved that any restricted blocked set formed from (LAMDA) is an I(,0)-set. Examples are given which show that these results are, in a certain sense, best possible. Finally if (LAMDA) (L-HOOK) Z('+), the positive integers, then it is shown that any blocked set formed from (LAMDA) is a Sidon subset of Z.^

#### Department(s)

Mathematics and Statistics

Thesis/Dissertation

Book

Citation

text

English