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Minimization with linear operators

Part I: Existence Theorems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 479)

Keywords

  • Banach Space
  • Minimization Problem
  • Convex Subset
  • Null Space
  • Spline Function

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References

  1. P. M. Anselone and P. J. Laurent, “A general method for the construction of interpolating or smoothing splines,” Numer. Math., 12 (1968), 66–82.

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  2. M. Atteia, “Fonctions splines defines sur un ensemble convexe,” Ibid. Math., 12 (1968), 192–210.

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  3. J. P. Aubin, “Interpolation et approximation optimales et ‘spline functions’,” J. Math. Anal. Appl., 24 (1968), 1–24.

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  4. N. Dunford and J. T. Schwartz, Linear Operators, Part I, Wiley Interscience, 1957.

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  5. S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.

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  6. M. Golomb and H. F. Weinberger, “Optimal approximation and error bounds,” in, On Numerical Approximation, (R. E. Langer, ed.), Univ. of Wisconsin Press, Madison, Wis., 1959, pp. 117–190.

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  7. J. Jerome and R. S. Varga, “Generalizations of spline functions and applications to nonlinear boundary value and eigenvalue problems”, in, Theory and Applications of Spline Functions, (T. N. E. Greville, editor), Academic Press, New York, 1969, pp. 103–155.

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  8. A. E. Taylor, Introduction to Functional Analysis, Wiley, New York, 1958.

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© 1975 Springer-Verlag

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Fisher, S.D., Jerome, J.W. (1975). Minimization with linear operators. In: Minimum Norm Extremals in Function Spaces. Lecture Notes in Mathematics, vol 479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097062

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  • DOI: https://doi.org/10.1007/BFb0097062

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07394-9

  • Online ISBN: 978-3-540-37599-9

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