Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
A CLASS OF I(,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.
Subject Area
Mathematics
Recommended Citation
GROW, DAVID EDWARD, "A CLASS OF I(,0)-SETS" (1981). ETD collection for University of Nebraska-Lincoln. AAI8127154.
https://digitalcommons.unl.edu/dissertations/AAI8127154