Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


A problem in convexity leading to the analysis of two functional equations

Author: John V. Ryff
Journal: Trans. Amer. Math. Soc. 305 (1988), 377-396
MSC: Primary 46A55; Secondary 28D05, 39B10, 47B38
MathSciNet review: 920165
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Transformation semigroups can often be studied effectively by examining their orbit structure. If the class of transformations has a special quality, such as convexity, it is generally reflected in the orbits. This work is concerned with such a circumstance. The goal is to examine the behavior of transformations on extreme points of orbits through the construction of a class of extreme operators. The construction leads naturally to the study of two functional equations which are analyzed in detail. Information about solutions is obtained through different $ {L^2}$-methods depending on whether or not two basic parameters are rational or irrational. In two cases all solutions are classified. In a third an example of a spanning set of solutions is obtained. Techniques of harmonic analysis and ergodic theory are used to study the functional equations.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46A55, 28D05, 39B10, 47B38

Retrieve articles in all journals with MSC: 46A55, 28D05, 39B10, 47B38

Additional Information

PII: S 0002-9947(1988)0920165-1
Keywords: Functional equations, convexity, extreme points, extreme operators, doubly stochastic, ergodic mappings, measure-preserving transformations
Article copyright: © Copyright 1988 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia