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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A problem in convexity leading to the analysis of two functional equations
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by John V. Ryff PDF
Trans. Amer. Math. Soc. 305 (1988), 377-396 Request permission


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.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 377-396
  • MSC: Primary 46A55; Secondary 28D05, 39B10, 47B38
  • DOI:
  • MathSciNet review: 920165