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Integrable resolvent operators for integrodifferential equations in Hilbert space

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Infinite-Dimensional Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1076))

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References

  1. Carr, R.W., K.B. Hannsgen: A nonhomogeneous integrodifferential equation in Hilbert Space, SIAM J. Math. Anal. 10 (1979), 961–984.

    Article  MathSciNet  MATH  Google Scholar 

  2. Carr, R.W., K.B. Hannsgen: Resolvent formulas for a Volterra equation in Hilbert space, SIAM J. Math. Anal. 13 (1982), 459–483.

    Article  MathSciNet  MATH  Google Scholar 

  3. Carslaw, H.S., J.C. Jaeger: Conduction of Heat in Solids, 2nd. ed., Clarendon Press, Oxford 1959.

    MATH  Google Scholar 

  4. DaPrato, G., M. Iannelli: Linear Integro-differential equations in Banach spaces, Rend. Sem. Mat. Univ. Padova 62 (1980), 207–219.

    MathSciNet  Google Scholar 

  5. DaPrato, G., M. Iannelli, E. Sinestrari: Temporal regularity for a class of integrodifferential equations in Banach spaces, Boll. U.M.I. An. Fur. Appl., to appear.

    Google Scholar 

  6. DaPrato, G., M. Iannelli, E. Sinestrari: Regularity of solutions of a class of linear integrodifferential equations in Banach spaces, to appear.

    Google Scholar 

  7. Friedman, A., M. Shinbrot: Volterra integral equations in Banach space, Trans. Amer. Math. Soc. 162 (1967), 131–179.

    Article  MathSciNet  MATH  Google Scholar 

  8. Grimmer, R.C.: Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273, 9 (1982), 333–349.

    Article  MathSciNet  MATH  Google Scholar 

  9. Grimmer, R.C., F. Kappel: Series expansions for resolvents of Volterra integrodifferential equations in Banach space, SIAM J. Math. Anal., to appear.

    Google Scholar 

  10. Grimmer, R.C., A.J. Pritchard: Analytic resolvent operators for integral equations in Banach space, J. Differential Equations, to appear.

    Google Scholar 

  11. Hannsgen, K.B.: A linear integrodifferential equation for viscoelastic rods and plates, Quarterly Appl. Math. 41 (1983), 75–83.

    MathSciNet  MATH  Google Scholar 

  12. Hannsgen, K.B., R.L. Wheeler: Complete monotonicity and resolvents of Volterra integrodifferential equations, SIAM J. Math. Anal. 13 (1982), 962–969.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hannsgen, K.B., R.L. Wheeler: A singular limit problem for an integrodifferential equation, J. Integral Equations 5 (1983), 199–209.

    MathSciNet  Google Scholar 

  14. Hannsgen, K.B., R.L. Wheeler: Uniform L1 behavior in classes of integrodifferential equations with completely monotonic kernels, SIAM J. Math. Anal., to appear.

    Google Scholar 

  15. Hannsgen, K.B., R.L. Wheeler: Behavior of the solution of a Volterra equation as a parameter tends to infinity, J. Integral Eqs., to appear.

    Google Scholar 

  16. MacCamy, R.C.: An integro-differential equation with application in heat flow, Quarterly Appl. Math. 35 (1977), 1–19.

    MathSciNet  MATH  Google Scholar 

  17. Miller, R.K., R.L. Wheeler: Asymptotic behavior for a linear Volterra integral equation in Hilbert space, J. Differential Equations 23 (1977), 270–284.

    Article  MathSciNet  MATH  Google Scholar 

  18. Widder, D.V.: The Laplace Transform, Princeton University Press, Princeton 1946.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute and State University, 24061, Blacksburg, Virginia, USA

    R. L. Wheeler

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  1. R. L. Wheeler
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Franz Kappel Wilhelm Schappacher

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© 1984 Springer-Verlag

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Wheeler, R.L. (1984). Integrable resolvent operators for integrodifferential equations in Hilbert space. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072781

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  • DOI: https://doi.org/10.1007/BFb0072781

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

  • eBook Packages: Springer Book Archive

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