RESOLVENT ESTIMATES FOR ABEL INTEGRAL OPERATORS AND THE REGULARIZATION OF ASSOCIATED FIRST KIND INTEGRAL EQUATIONS

RESOLVENT ESTIMATES FOR ABEL INTEGRAL OPERATORS AND THE REGULARIZATION OF ASSOCIATED FIRST KIND INTEGRAL EQUATIONS

In this paper resolvent estimates for Abel integral operators are provided. These estimates are applied to deduce regularizing properties of Lavrentiev's m-times iterated method as well as iterative schemes (with the discrepancy principle as corresponding parameter choice or stopping rule, resp...

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Veröffentlicht in:The Journal of integral equations and applications 1997, Vol.9 (3), p.253-278
1. Verfasser: PLATO, R.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Differential equations
Hilbert spaces
Integers
Iterative methods
Linear transformations
Mathematical functions
Mathematical integrals
Semigroups
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Zusammenfassung:In this paper resolvent estimates for Abel integral operators are provided. These estimates are applied to deduce regularizing properties of Lavrentiev's m-times iterated method as well as iterative schemes (with the discrepancy principle as corresponding parameter choice or stopping rule, respectively) for solving the corresponding Abel integral equations of the first kind.
ISSN:0897-3962
1938-2626
DOI:10.1216/jiea/1181076015