On the resolvent of a linear operator associated with a wellposed Cauchy problem
Author:
John Miller
Journal:
Math. Comp. 22 (1968), 541548
MSC:
Primary 47.30; Secondary 35.00
MathSciNet review:
0233220
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We show how local estimates may be obtained for holomorphic functions of a class of linear operators on a finitedimensional linear vector space. This is accomplished by classifying the spectrum of each operator and then estimating its resolvent on certain contours in the left halfplane. 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 powerbounded operators are given in [3].
 [1]
HeinzOtto
Kreiss, Über Matrizen die beschränkte Halbgruppen
erzeugen, Math. Scand. 7 (1959), 71–80
(German). MR
0110952 (22 #1820)
 [2]
John
Miller and Gilbert
Strang, Matrix theorems for partial differential and difference
equations, Math. Scand. 18 (1966), 113–133. MR 0209308
(35 #206)
 [3]
John
J. H. Miller, On powerbounded operators and operators satisfying a
resolvent condition, Numer. Math. 10 (1967),
389–396. MR 0220080
(36 #3147)
 [4]
K.
W. Morton, On a matrix theorem due to H. O. Kreiss, Comm. Pure
Appl. Math. 17 (1964), 375–379. MR 0170460
(30 #698)
 [1]
 H.O. Kreiss, ``Über Matrizen die beschränkte Halbgruppen erzeugen,'' Math. Scand., v. 7, 1959, pp. 7180. MR 0110952 (22:1820)
 [2]
 John Miller & Gilbert Strang, ``Matrix theorems for partial differential and difference equations,'' Math. Scand., v. 18, 1966, pp. 113133. MR 35 #206. MR 0209308 (35:206)
 [3]
 John Miller, ``On powerbounded operators and operators satisfying a resolvent condition,'' Numer. Math., v. 10, 1967, pp. 389396. MR 0220080 (36:3147)
 [4]
 K. W. Morton, ``On a matrix theorem due to H.O. Kreiss,'' Comm. Pure Appl. Math., v. 17, 1965, pp. 375380. MR 30 #698. MR 0170460 (30:698)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
47.30,
35.00
Retrieve articles in all journals
with MSC:
47.30,
35.00
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819680233220X
PII:
S 00255718(1968)0233220X
Article copyright:
© Copyright 1968
American Mathematical Society
