Abstract
Compact operators cannot have a bounded inverse. Therefore, equations of the first kind with a compact operator provide a typical example for socalled ill-posed problems.In this chapter we introduce regularization methods for the stable solution of equations of the first kind in a Hilbert space setting. For a more comprehensive study of ill-posed problems, we refer to Baumeister [13], Engl, Hanke, and Neubauer [38], Groetsch [58], Kirsch [87], Louis [116], Morozov [129], and Tikhonov and Arsenin [174].
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© 1999 Springer Science+Business Media New York
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Kress, R. (1999). Equations of the First Kind. In: Linear Integral Equations. Applied Mathematical Sciences, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0559-3_15
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DOI: https://doi.org/10.1007/978-1-4612-0559-3_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6817-8
Online ISBN: 978-1-4612-0559-3
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