Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Representation of linear functionals on quasi-continuous functions

Author: James D. Baker
Journal: Proc. Amer. Math. Soc. 48 (1975), 120-124
MSC: Primary 46E15
MathSciNet review: 0374884
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The question of representing the continuous linear functionals on the complex quasi-continuous functions in terms of a single integral of Stieltjes type is considered. An integral on three functions is defined, is shown to provide a unique representation of the functionals, and in special cases, is shown to reduce to standard Stieltjes integrals involving two functions.

References [Enhancements On Off] (What's this?)

  • [1] H. S. Kaltenborn, Linear functional operations on functions having discontinuities of the first kind, Bull. Amer. Math. Soc. 40 (1934), 702-708. MR 1562957
  • [2] R. E. Lane, Linear operators on quasi-continuous functions, Trans. Amer. Math. Soc. 89 (1958), 378-394. MR 20 #5416. MR 0098971 (20:5416)
  • [3] W. W. Schmaedeke and G. R. Sell, The Gronwall inequality for modified Stieltjes integrals, Proc. Amer. Math. Soc. 19 (1968), 1217-1222. MR 37 #6422. MR 0230864 (37:6422)
  • [4] F. M. Wright and J. D. Baker, On integration-by-parts for weighted integrals, Proc. Amer. Math. Soc. 22 (1969), 42-52. MR 39 #7056. MR 0245750 (39:7056)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E15

Retrieve articles in all journals with MSC: 46E15

Additional Information

Keywords: Stieltjes integrals, quasi-continuous functions, linear functionals
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society