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

Embedding Stieltjes-Volterra integral equations in Stieltjes integral equations


Author: William L. Gibson
Journal: Trans. Amer. Math. Soc. 227 (1977), 263-277
MSC: Primary 45D05
MathSciNet review: 0430695
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Abstract: J. A. Reneke has shown that the linear Stieltjes-Volterra integral equations studied by D. B. Hinton can be transformed into Stieltjes integral equations of the type studied by J. S. Mac Nerney. By taking advantage of the nonlinear nature of Mac Nerney's results, Reneke was able to extend Hinton's existence theorem to a nonlinear setting. In this paper, we use Reneke's embedding technique to generalize several other of Hinton's results, and we characterize completely, in the linear case, the range of Reneke's embedding transformation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0430695-X
PII: S 0002-9947(1977)0430695-X
Keywords: Stieltjes-Volterra integral equations, nonlinear integration by substitution, hereditary system, quasicontinuous functions
Article copyright: © Copyright 1977 American Mathematical Society