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Transactions of the American Mathematical Society

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

 
 

 

A pairing of a class of evolution systems with a class of generators.


Author: J. V. Herod
Journal: Trans. Amer. Math. Soc. 157 (1971), 247-260
MSC: Primary 47.70
DOI: https://doi.org/10.1090/S0002-9947-1971-0281059-8
MathSciNet review: 0281059
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Abstract: Suppose that $S$ is a Banach space and that $A$ and $M$ are functions such that if $x$ and $y$ are numbers, $x \geqq y$, and $P$ is in $S$ then each of $M(x,y)P$ and $A(y,P)$ is in $S$. This paper studies the relation \[ M(x,y)P = P + \int _x^y {A(t,M(t,y)P)dt.} \] Classes OM and OA will be described and a correspondence will be established which pairs members of the two classes which are connected as $M$ and $A$ are by the relation indicated above.


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Keywords: Nonlinear evolution systems, expansive evolution systems, product integration
Article copyright: © Copyright 1971 American Mathematical Society