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A Volterra equation with nonintegrable resolvent


Author: Gustaf Gripenberg
Journal: Proc. Amer. Math. Soc. 73 (1979), 57-60
MSC: Primary 45D05; Secondary 45E10
DOI: https://doi.org/10.1090/S0002-9939-1979-0512058-9
MathSciNet review: 512058
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Abstract: A counterexample, which shows that the resolvent associated with a nonnegative, nonincreasing function need not be integrable, is constructed.


References [Enhancements On Off] (What's this?)

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  • [3] G. S. Jordan and R. L. Wheeler, A generalization of the Wiener-Lévy theorem applicable to some Volterra equations, Proc. Amer. Math. Soc. 57 (1976), 109-114. MR 0405023 (53:8819)
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  • [6] R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., vol. 19, Amer. Math. Soc., Providence, R. I., 1934; reprinted 1973. MR 1451142 (98a:01023)
  • [7] D. F. Shea and S. Wainger, Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations, Amer. J. Math. 97 (1975), 312-343. MR 0372521 (51:8728)
  • [8] O. J. Staffans, On the integrability of the resolvent of a Volterra equation, Report-HTKK-MAT-A103, Helsinki Univ. of Technology, 1977.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0512058-9
Article copyright: © Copyright 1979 American Mathematical Society

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