Vol. 70, No. 1, 1977

Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
The theory of almost periodic functions in constructive mathematics

James Dennis Brom

Vol. 70 (1977), No. 1, 67–81
Abstract

In this paper we develop a constructive theory of continuous almost periodic functions. We expose those aspects of the standard theory that are not constructive and give constructive substitutes. For example, it is not true in constructive mathematics that each trigonometric polynomial is almost periodic. A trigonometric polynomial is almost periodic if and only if its exponents are rationally discrete. We obtain a constructive proof of Bohr’s fundamental theorem that leads to a computational method for uniform approximations to continuous almost periodic functions by trigonometric polynomials.

Mathematical Subject Classification
Primary: 02E05, 02E05
Secondary: 42A84
Milestones
Received: 13 October 1976
Published: 1 May 1977
Authors
James Dennis Brom