Volume 58, pp. 517-537, 2023.

A Gauss-Laguerre approach for the resolvent of fractional powers

Eleonora Denich, Laura Grazia Dolce, and Paolo Novati


This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbounded) self-adjoint positive operators in Hilbert spaces. The method is based on the Gauss-Laguerre rule, exploiting a particular integral representation of the resolvent. We provide sharp error estimates that can be used to a priori select the number of nodes to achieve a prescribed tolerance.

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Key words

resolvent of fractional powers, Gauss-Laguerre rule, functions of operators

AMS subject classifications

47A58, 65F60, 65D32

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