On the resolvent of a linear operator associated with a well-posed Cauchy problem
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- by John Miller PDF
- Math. Comp. 22 (1968), 541-548 Request permission
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].References
- Heinz-Otto Kreiss, Über Matrizen die beschränkte Halbgruppen erzeugen, Math. Scand. 7 (1959), 71–80 (German). MR 110952, DOI 10.7146/math.scand.a-10563
- John Miller and Gilbert Strang, Matrix theorems for partial differential and difference equations, Math. Scand. 18 (1966), 113–133. MR 209308, DOI 10.7146/math.scand.a-10786
- John J. H. Miller, On power-bounded operators and operators satisfying a resolvent condition, Numer. Math. 10 (1967), 389–396. MR 220080, DOI 10.1007/BF02162872
- K. W. Morton, On a matrix theorem due to H. O. Kreiss, Comm. Pure Appl. Math. 17 (1964), 375–379. MR 170460, DOI 10.1002/cpa.3160170310
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 541-548
- MSC: Primary 47.30; Secondary 35.00
- DOI: https://doi.org/10.1090/S0025-5718-1968-0233220-X
- MathSciNet review: 0233220