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Volterra-Stieltjes integral equations with linear constraints and discontinuous solutions


Author: Chaim Samuel Hönig
Journal: Bull. Amer. Math. Soc. 81 (1975), 593-598
MSC (1970): Primary 34G05, 45A05, 34A30, 45D05, 34B05; Secondary 26A45, 26A42, 28A45
MathSciNet review: 0377219
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  • B. H. E. Bray, Elementary properties of Stieltjes integral, Ann. of Math. 20 (1918/19), 177-186.
  • N. Dinculeanu, Vector measures, International Series of Monographs in Pure and Applied Mathematics, Vol. 95, Pergamon Press, Oxford-New York-Toronto, Ont.; VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. MR 0206190
  • G. M. Gowurin, Über die Stieltjes Integration abstrakter Funktionen, Fund. Math. 27 (1936), 255-268.
  • T. H. Hildebrandt, Introduction to the theory of integration, Pure and Applied Mathematics, Vol. XIII, Academic Press, New York-London, 1963. MR 0154957
  • Chaim Samuel Hönig, The Green function of a linear differential equation with a lateral condition, Bull. Amer. Math. Soc. 79 (1973), 587–593. MR 0312019, 10.1090/S0002-9904-1973-13214-8
  • Chaim Samuel Hönig, The abstract Riemann-Stieltjes integral and its applications to linear differential equation with generalized boundary conditions, Universidade de S ao Paulo. S ao Paulo, 1973. Notas do Instituto de Matemática e Estatística da Universidade de S ao Paulo, Série Matemática, No. 1. [Notes of the Institute of Mathematics and Statistics of the University of S ao Paulo, Mathematics Series, No. 1]. MR 0460561
  • Chaim Samuel Hönig, Volterra Stieltjes-integral equations, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. Functional analytic methods; linear constraints; Mathematics Studies, No. 16; Notas de Matemática, No. 56. [Notes on Mathematics, No. 56]. MR 0499969
  • K. H. S. Kaltenborn, Linear functional operations on functions having discontinuities of the first kind, Bull. Amer. Math. Soc. 40 (1934), 702-708.
  • J. S. MacNerney, Stieltjes integrals in linear spaces, Ann. of Math. (2) 61 (1955), 354–367. MR 0067354

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Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1975-13749-9