Functional Analysis and Differential Equations in Abstract Spaces provides an elementary treatment of this very classical topic-but presented in a rather unique way. The author offers the functional analysis interconnected with specialized sections on differential equations, thus creating a self-contained text that includes most of the necessary functional analysis background, often with quite complete proofs.
Beginning with some basic functional analysis-Hilbert and Banach spaces and their linear operators-Dr. Zaidman then presents some results about the abstract Cauchy problem, in implicit or explicit form, and related semigroups of operators, weak and ultraweak solutions, the uniqueness of the Cauchy problem, the uniqueness of bounded ultraweak solutions, and the well-posed ultraweak
Cauchy problem. He goes on to present some results on almost-periodic solutions and an asymptotic result for a differential inequality in ultraweak form.
Designed to inspire interest in this elegant and rapidly growing field of mathematics, this volume presents the material at a relatively elementary level-requiring a minimum of knowledge and ability in the field-yet with depth sufficient for understanding various special topics in operator differential equations. Many of the research results appear for the first time in book form and some for the first time anywhere. Researchers in the theories of differential equations in abstract spaces, semigroups of operators, and evolution equations, along with researchers in mathematical physics and quantum mechanics will find this work both enlightening and accessible.