Linear Differential Equations and Function Spaces (Pure and Applied Mathematics, Vol 2)

Description

This book presents in systematic and detailed form the recent studies of the authors concerning linear ordinary differential equations in the real domain.

Rounding off the development of an idea going back to the work of O. Perron (1930), the theory prsented here thoroughly discusses, in the central part of the book, relations between properties of the non-homogeneous equation - typically, ``admissibility" of a pair of function spaces, i.e., the property of the equation having, for each ``second member" in one space, at least one solution in the other - and the behavior of the solutions of the homogeneous equation - typically a ``dichotomy" or an ``exponential dichotomy", i.e., a kind of uniform conditional stability, ordinary or asymptotic, respectively. There are additional chapters on several connected topics, e.g., almost periodic equations and periodic equations.

Considerable emphasis is placed on the methods of functional analysis and on the use of function spaces. The theory is developed for equations in a Banach space, but its significance does not depend on this generalization of the usual finite-dimensional setting.

The book is addressed primarily to readers interested in ordinary differential equations, who will be best prepared to understand its motivation; but no specialized knowledge in this field is required. In functional analysis, a working aquaintance with Banach-space theory, both ``soft" and ``hard" (but no intimate knowledge of operator theory) is assumed.




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