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The main purpose of this book is to introduce the generalized
composition operators and the generalized multiplication operators
on weighted Hardy spaces . Composition operators have been the
subject matter of intensive study over past several decades and
they find applications in ergodic theory, quantum mechanics and
other branches of mathematical and physical sciences . The 1st
chapter of the book contains introductory material . The compact,
Fredholm generalized composition operators are characterized in the
second chapter. The Hermitian, Normal, Quasi normal, Isometric and
co isometric generalized composition operators are presented in the
third chapter. It is shown that most of the properties of the
generalized multiplication operators differ from the multiplication
operators acting on other function spaces .eg: - On most of the
function spaces multiplication operators are normal .But this
result is not valid incase of generalized multiplication operators
on weighted Hardy spaces . In this book some light is thrown on
differential and anti-differential operators acting on weighted
Hardy spaces .
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