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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the resolvent of a linear operator associated with a well-posed Cauchy problem

Author: John Miller
Journal: Math. Comp. 22 (1968), 541-548
MSC: Primary 47.30; Secondary 35.00
MathSciNet review: 0233220
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Abstract: We show how local estimates may be obtained for holomorphic functions of a class of linear operators on a finite-dimensional linear vector space. This is accomplished by classifying the spectrum of each operator and then estimating its resolvent on certain contours in the left half-plane. We apply these methods to prove some known theorems, and in addition we obtain new estimates for the inverse of these operators. Analogous results for power-bounded operators are given in [3].

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Article copyright: © Copyright 1968 American Mathematical Society