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Excerpt from Linear Differential Equations in Banach Spaces Here t is a real variable; the unknown function u(t) and the given function f(t) take values in a Banach space X; and A(t) is a given function whose values are linear operators in X. We wish to find the solution of or (l.la) when the initial value u(a) is prescribed. The problem is rather trivial if the operators A(t) are bounded* and, say, strongly continuous in t, for then the solution can be obtained by a standard iteration procedure. But we are mainly interested in the case where the Mt) are unbounded, so that their domains are proper subsets of X. In such a case the existence of the solution is by no means obvious. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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