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Representation of additive and biadditive functionals

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References

  1. Martin, A. D., & V. J. Mizel, A representation theorem for certain nonlinear functionals. Arch. Rational Mech. Anal. 15, 353–367 (1964).

    Google Scholar 

  2. Chacon, R. V., & N. Friedman, Additive functionals. Arch. Rational Mech. Anal. 18, 230–240 (1965).

    Google Scholar 

  3. Friedman, N., & M. Katz, Additive functionals. Canadian J. of Math. XVIII, 1264–1271 (1966).

    Google Scholar 

  4. Coleman, B. D., & V. J. Mizel, Norms and semi-groups in the theory of fading memory. Arch. Rational Mech. Anal. 23, 87–123 (1966).

    Google Scholar 

  5. Halmos, P. R., Functions of integrable functions. J. Indian Math. Soc. 11, 81–84 (1947).

    Google Scholar 

  6. Dunford, N., & J. T. Schwartz, Linear Operators, Part I. New York: Interscience 1958.

    Google Scholar 

  7. Bartle, R. G., & J. R. Joichi, The preservation of convergence of measurable functions under composition. Proc. Amer. Math. Soc. 12, 122–126 (1961).

    Google Scholar 

  8. Bartle, R. G., The Elements of Integration. New York: John Wiley and Sons 1966.

    Google Scholar 

  9. Morse, M., & W. Transue, Integral representations of bilinear functionals. Proc. Nat. Acad. Sci. U.S.A. 35, 136–143 (1949).

    Google Scholar 

  10. Luxemburg, W., Banach Function Spaces. Thesis, Technische Hoge-School te Delft, 1955.

  11. Zaanen, A. C., Linear Analysis. Amsterdam: North Holland Publishing Co. 1956.

    Google Scholar 

  12. Gelfand, I. M., & N. Ya. Vilenkin, Generalized Functions, Vol. 4, pp. 273–278. New York: Academic Press 1964.

    Google Scholar 

  13. Krasnosel'skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations, (Translation), Chapter 1, § 2. New York: Macmillan 1964.

    Google Scholar 

  14. Caratheodory, C., Vorlesungen über Relle Functionen, 2nd edition, §§ 576, 577. Leipzig and Berlin: B. G. Teubner 1927.

    Google Scholar 

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Authors and Affiliations

  1. Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA

    V. J. Mizel & K. Sundaresan

  2. University of Missouri, Columbia, Missouri, USA

    V. J. Mizel & K. Sundaresan

Authors
  1. V. J. Mizel
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  2. K. Sundaresan
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Additional information

Communicated by Walter Noll

This work was partially supported by NSF Grant GP-6173.

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Mizel, V.J., Sundaresan, K. Representation of additive and biadditive functionals. Arch. Rational Mech. Anal. 30, 102–126 (1968). https://doi.org/10.1007/BF00250940

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  • DOI: https://doi.org/10.1007/BF00250940

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