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 .
- Heinz-Otto Kreiss, Über Matrizen die beschränkte Halbgruppen erzeugen, Math. Scand. 7 (1959), 71–80 (German). MR 110952, DOI https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1002/cpa.3160170310
H.-O. Kreiss, “Über Matrizen die beschränkte Halbgruppen erzeugen,” Math. Scand., v. 7, 1959, pp. 71–80.
John Miller & Gilbert Strang, “Matrix theorems for partial differential and difference equations,” Math. Scand., v. 18, 1966, pp. 113–133. MR 35 #206.
John Miller, “On power-bounded operators and operators satisfying a resolvent condition,” Numer. Math., v. 10, 1967, pp. 389–396.
K. W. Morton, “On a matrix theorem due to H.-O. Kreiss,” Comm. Pure Appl. Math., v. 17, 1965, pp. 375—380. MR 30 #698.