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Proceedings of the American Mathematical Society

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

 

 

Absolutely continuous component of a class of integral operators


Author: Richard E. Sours
Journal: Proc. Amer. Math. Soc. 37 (1973), 521-524
MSC: Primary 47G05
DOI: https://doi.org/10.1090/S0002-9939-1973-0312333-1
MathSciNet review: 0312333
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Abstract: The operator $ T:{L^2}(0,\infty ) \to {L^2}(0,\infty )$ defined by

$\displaystyle Tf(x) = \int_0^\infty {\frac{{k(x){{(k(t))}^ - }}}{{x + t}}} \;f(t)\;dt,$

where $ {(k(t))^ - }$ is the complex conjugate, is studied and conditions are given which are sufficient to characterize the absolutely continuous component.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312333-1
Keywords: Integral operator, commutator systems, absolutely continuous component
Article copyright: © Copyright 1973 American Mathematical Society