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Ill-Posedness in the 1-Setting

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Part of the book series: Frontiers in Mathematics ((FM))

Abstract

We discuss ill-posedness of linear operator equations in the 1-setting and show that this setting makes all linear equations ill-posed in the sense of Nashed.

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References

  1. M.Z. Nashed, in Inverse and Ill-posed Problems (Sankt Wolfgang, 1986), volume 4 of Notes and Reports in Mathematics in Science and Engineering (Academic Press, Boston, MA, 1987), pp. 53–75

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  2. R.E. Megginson, An Introduction to Banach Space Theory, Graduate Texts in Mathematics, vol. 183 (Springer, New York, 1998)

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  3. J. Flemming, B. Hofmann, I. Veselić, Computational Methods in Applied Mathematics 15, 279 (2015)

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  4. M. Takesaki, Theory of Operator Algebra I, Encyclopaedia of Mathematical Sciences, vol. 124 (Springer, Berlin Heidelberg New York, 2002)

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  5. S. Goldberg, E. Thorp, Proc. Amer. Math. Soc. 14, 334 (1963)

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Flemming, J. (2018). Ill-Posedness in the 1-Setting. In: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-95264-2_10

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