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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
DOI: https://doi.org/10.1090/S0002-9904-1975-13749-9
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, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
    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.
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  • 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, https://doi.org/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.
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Additional Information

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