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.

**[1]**G. Gripenberg,*Integrability properties of resolvents of Volterra equations*, Report-HTKK-MAT-A117, Helsinki Univ. of Technology, 1978.**[2]**S. I. Grossman,*Integrability of resolvents of certain Volterra integral equations*, J. Math. Anal. Appl.**48**(1974), 785-793. MR**0352909 (50:5395)****[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)****[4]**J. J. Levin,*Resolvents and bounds for linear and nonlinear Volterra equations*, Trans. Amer. Math. Soc.**228**(1977), 207-222. MR**0433162 (55:6141)****[5]**R. K. Miller,*On Volterra integral equations with nonnegative integrable resolvents*, J. Math. Anal. Appl.**22**(1968), 319-340. MR**0227707 (37:3291)****[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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DOI:
https://doi.org/10.1090/S0002-9939-1979-0512058-9

Article copyright:
© Copyright 1979
American Mathematical Society