This book is the first to be devoted to the theory of vector-valued
functions with one variable. This theory is one of the fundamental tools
employed in modern physics, the spectral theory of operators,
approximation of analytic operators, analytic mappings between vectors,
and vector-valued functions of several variables.
The book contains three chapters devoted to the theory of normal
functions, Hp-space, and vector-valued functions and their
applications. Among the topics dealt with are the properties of complex
functions in a complex plane and infinite-dimensional spaces, and the
solution of vector-valued integral equations and boundary value problems
by complex analysis and functional analysis, which involve methods which
can be applied to problems in operations research and control theory.
Much original research is included.
This volume will be of interest to those whose work involves complex
analysis and control theory, and can be recommended as a graduate text
in these areas.