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Nonlinear volterra functional equations and linear parabolic differential systems

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Bibliography

  1. R. H. Cameron, The generalized heat flow equation and a corresponding Poisson formula.Annals of Math. 59 (1954), pp. 434–462.

    Article  Google Scholar 

  2. R. H. Cameron, and R. E. Fagen, Nonlinear transformations of Volterra type in Wiener space.Trans. Amer. Math. Soc. 75 (1953), pp. 552–575.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. H. Cameron and W. T. Martin, Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations.Bull. Amer. Math. Soc. 51 (1945), pp. 73–89.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations.Annals of Math., 45 (1944), pp. 386–396.

    Article  MathSciNet  Google Scholar 

  5. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformationsTrans. Amer. Math. Soc. 58 (1945), pp. 184–219.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. H. Cameron and W. T. Martin, The transformations of Wiener integrals by nonlinear transformations.Trans. Amer. Math. Soc. 66 (1949), pp. 253–283.

    Article  MATH  MathSciNet  Google Scholar 

  7. R. H. Cameron and J. M. Shapiro, Nonlinear Integral Equations.Annals of Math., 62 (1955), pp. 472–497.

    Article  MathSciNet  Google Scholar 

  8. E. H. Cuthill, Integrals on spaces of functions which are real and continuous on finite and infinite intervals.Thesis, Univ. of Minn., Dec. 1953.

  9. D. A. Darley and A. J. F. Siegert, Integral equations for the characteristic functions of certain functionals of multidimensional Markoff processes.Rand report p. 429 (Oct. 31, 1953) Rand Corp., Santa Monica, Cal.

    Google Scholar 

  10. W. Feller, Zur Theorie der stochastischen Prozesse.Math. Ann. 113 (1937), pp. 113–159.

    Article  MathSciNet  Google Scholar 

  11. R. Fortet, Les fonctions aléatoires du type Markoff associées à certaines équations linéaires aux dérivées partielles du type parabolique.J. Math. Pures et Appliquées, 22 (1943), pp. 177–243.

    MATH  MathSciNet  Google Scholar 

  12. K. Ito, On stochastic Differential Equations.Mem. Amer. Math. Soc. 4 (1951), pp. 1–51.

    Google Scholar 

  13. M. Kac, On distributions of certain Wiener functionals.Trans. Amer. Math. Soc. 65 (1949), pp. 1–13.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Kolmogoroff, Zur Theorie der stetigen zufälligen Prozesse.Math. Ann. 108 (1933), pp. 149–160.

    Article  MathSciNet  Google Scholar 

  15. M. Rosenblatt, On a class of Markoff processes.Trans. Amer. Math. Soc. 71 (1951), pp. 120–135.

    Article  MATH  MathSciNet  Google Scholar 

  16. W. E. Strimling, Solution of a linear second order partial differential equation in three variables by Wiener integration.Thesis, Univ. of Minn., Dec. 1953.

  17. A. J. Tingley, A generalization of the Poisson formula for the solution of the heat flow equation.Proc. Amer. Math. Soc., 7 (1956), pp. 846–851.

    Article  MATH  MathSciNet  Google Scholar 

  18. N. Wiener, Generalized harmonic Analysis.Acta. Math. 55 (1930), pp. 117–258, esp. pp. 214–234.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. The University of Minnesota, Minneapolis, Minnesota, U.S.A.

    R. H. Cameron

  2. The Institute for Advanced Study, Minneapolis, Minnesota, U.S.A.

    R. H. Cameron

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  1. R. H. Cameron
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Additional information

This research was supported by the United States Air Force, through the Office of Scientific Research of the Air Research and Development Command. Presented to the American Mathematical Society, December 1955.

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Cameron, R.H. Nonlinear volterra functional equations and linear parabolic differential systems. J. Anal. Math. 5, 136–182 (1956). https://doi.org/10.1007/BF02937344

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