Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Composition operators induced by rational functions


Author: R. K. Singh
Journal: Proc. Amer. Math. Soc. 59 (1976), 329-333
MSC: Primary 47B37
MathSciNet review: 0417847
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Abstract: A necessary and sufficient condition for a rational function to define a composition operator on $ {L^p}(\mu )$ is given in this paper, where $ \mu $ is the Lebesgue measure on the Borel subsets of the real line. In particular, all polynomials inducing composition operators are completely determined.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0417847-4
Keywords: Rational functions, composition operators, polynomials, derivative
Article copyright: © Copyright 1976 American Mathematical Society