Pacific Journal of Mathematics

Regular operator approximation theory.

P. M. Anselone and M. L. Treuden

Article information

Pacific J. Math., Volume 120, Number 2 (1985), 257-268.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A50: Equations and inequalities involving linear operators, with vector unknowns
Secondary: 65J10: Equations with linear operators (do not use 65Fxx)


Anselone, P. M.; Treuden, M. L. Regular operator approximation theory. Pacific J. Math. 120 (1985), no. 2, 257--268.

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  • [I] P. M. Anselone, Collectively Compact Operator Approximation Theory, Prentice-Hall, 1971.
  • [2] P. M. Anselone, Singularity subtraction in the numerical solution of integral equations, J. Austral. Math. So,(Series B) 22 (1981),408-418.
  • [3] P. M. Anselone and R. Ansorge, Compactness principles in nonlinear operator approximation theory, Numer. Funct. Anal, and Optim., 1 (6),(1979),598-618.
  • [4] P. M. Anselone and R. Ansorge, A unified framework for the discretization of nonlinear operator equations, Numer. Funct. Anal, and Optim., 4 (1),(1981),61-99.
  • [5] K. E. Atkinson, A survey of numerical methods for the solution of Fredholm integral equations of the second kind, SIAM Publications, 1976.
  • [6] F. Chatelin, The spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators, SIAM Review, 23 (1981), 495-522.
  • [7] R. D. Grigorieff, Zur TheorieLinearer approximations regularer Operatoren /, Math. Nachr., 55 (1973),233-249.
  • [8] R. D. Grigorieff, Zur Theorie Linearer approximations regularer Operatoren II, Math. Nachr., 55 (1973), 251-263.
  • [9] T. Kato, Perturbation Theoryfor Linear Operators, 2nd Ed., Springer-Verlag,1976.
  • [10] F. Stummel, Discrete convergence of mappings, Proc. Conf. Numer. Anal., Dublin, 1972, pp. 285-310, AcademicPress,1973.
  • [II] A. E. Taylor and D. C. Lay, Introduction to FunctionalAnalysis, Wiley, 1980.
  • [12] G. Vainikko, Funktionalanalysis der Diskretisierungsmethoden, Teubner, Leipzig, 1976.
  • [13] R. Wolf, Uber lineare approximationsregulre Operatoren, Math. Nachr., 59 (1974), 325-341.
  • [14] B. Yood, Properties of linear transformationspreserved under addition of a completely continuous transformation, Duke Math. J., 18 (1951),599-612.