A Tauberian problem for a Volterra integral operator
Author:
Gustaf Gripenberg
Journal:
Proc. Amer. Math. Soc. 82 (1981), 576-582
MSC:
Primary 45D05; Secondary 40E05
DOI:
https://doi.org/10.1090/S0002-9939-1981-0614881-8
MathSciNet review:
614881
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Abstract | References | Similar Articles | Additional Information
Abstract: The following question is studied: For which (nonintegrable) kernels does
imply that
when
is bounded and satisfies a Tauberian condition.
- [1] W. F. Donoghue, Distributions and Fourier transforms, Academic Press, New York, 1969.
- [2] G. Gripenberg, A Volterra equation with nonintegrable resolvent, Proc. Amer. Math. Soc. 73 (1979), 57-60. MR 512058 (80b:45001)
- [3] -, Integrability of resolvents of systems of Volterra equations, SIAM J. Math. Anal. (to appear). MR 617717 (84a:45005)
- [4] 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)
- [5] J. J. Levin and D. F. Shea, On the asymptotic behavior of the bounded solutions of some integral equations. I, J. Math. Anal. Appl. 37 (1972), 42-82. MR 0306849 (46:5971)
- [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. MR 1451142 (98a:01023)
- [7] W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974. MR 0344043 (49:8783)
- [8] 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)
- [9] O. J. Staffans, On the integrability of the resolvent of a Volterra equation, Report-HTKK-MAT-A103, Helsinki University of Technology, Espoo, Finland, 1977.
- [10] D. V. Widder, The Laplace transform, Princeton Univ. Press, Princeton, N.J., 1946.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1981-0614881-8
Article copyright:
© Copyright 1981
American Mathematical Society