References
H.-O. Kreiss, Über Matrizen die beschränkte Halbgruppen erzeugen,Math. Scand.,7 (1959) 71–80.
T. Kato and H. Tanabe, On the abstract evolution equation,Osaka Math. J.,14 (1962) 107–133.
T. Kato and H. Tanabe, On the analyticity of solutions of evolution equations,Osaka Math. J.,4 (1967) 1–4.
H. Tanabe, Evolution equations of parabolic type,Proc. Japan Acad.,37 (1961) 610–613.
P. E. Sobolevski, Parabolic type equations in Banach spaces,Trudy Moscow Math.,10 (1961) 297–350.
H.-O. Kreiss, Über die Stabilitätsdefinition für Differenzengleichungen die partielle Differentialgleichungen approximieren,BIT 2 (1962) 153–181.
K. W. Morton and S. Schechter, On the stability of finite difference matrices,SIAM J. Num. Analysis,2 (1965) 119–128.
R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, Interscience, New York, 1967.
K. W. Morton, On a matrix theorem due to H.-O. Kreiss,Comm. Pure Appl. Math.,17 (1965) 375–380.
J. Miller and G. Strang, Matrix theorems for partial differential and difference equations,Math. Scand.,18 (1966) 113–133.
J. Miller, On power-bounded operators and operators satisfying a resolvent condition,Numer. Math.,10 (1967) 389–396.
V. Thomée, Parabolic difference operators,Math. Scand.,19 (1966) 77–107.
Author information
Authors and Affiliations
Additional information
This research was supported by the Office of Naval Research and the National Science Foundation (GP 7477).
Rights and permissions
About this article
Cite this article
Strang, G. On numerical ranges and holomorphic semigroups. J. Anal. Math. 22, 299–318 (1969). https://doi.org/10.1007/BF02786795
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02786795