Dichotomy and H∞ Functional Calculi
Date
1995-09-21
Authors
DeLaubenfels, R.
Latushkin, Y.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Dichotomy for the abstract Cauchy problem with any densely defined closed operator on a Banach space is studied. We give conditions under which an operator with an H∞ functional calculus has dichotomy. For the operators with imaginary axis contained in the resolvent set and with polynomial growth of the resolvent along the axis we prove the existence of dichotomy on subspaces and superspaces. Applications to the dichotomy of operators on Lp- spaces are given. The principle of linearized instability for nonlinear equations is proved.
Description
Keywords
Abstract Cauchy problem, Operator semigroups, Exponential dichotomy, Functional calculi
Citation
DeLaubenfels, R. & Latushkin, Y. (1995). Dichotomy and H∞ Functional Calculi. <i>Electronic Journal of Differential Equations, 1995</i>(13), pp. 1-17.
Rights
Attribution 4.0 International