Linear Functional Analysis For Scientists And Engineers
by Balmohan V. Limaye /
2016 / English / PDF
3.1 MB Download
This book provides a concise and meticulous introduction to
functional analysis. Since the topic draws heavily on the
interplay between the algebraic structure of a linear space and
the distance structure of a metric space, functional analysis is
increasingly gaining the attention of not only mathematicians but
also scientists and engineers. The purpose of the text is to
present the basic aspects of functional analysis to this varied
audience, keeping in mind the considerations of applicability. A
novelty of this book is the inclusion of a result by Zabreiko,
which states that every countably subadditive seminorm on a
Banach space is continuous. Several major theorems in functional
analysis are easy consequences of this result.
This book provides a concise and meticulous introduction to
functional analysis. Since the topic draws heavily on the
interplay between the algebraic structure of a linear space and
the distance structure of a metric space, functional analysis is
increasingly gaining the attention of not only mathematicians but
also scientists and engineers. The purpose of the text is to
present the basic aspects of functional analysis to this varied
audience, keeping in mind the considerations of applicability. A
novelty of this book is the inclusion of a result by Zabreiko,
which states that every countably subadditive seminorm on a
Banach space is continuous. Several major theorems in functional
analysis are easy consequences of this result.
The entire book can be used as a textbook for an introductory
course in functional analysis without having to make any specific
selection from the topics presented here. Basic notions in the
setting of a metric space are defined in terms of sequences.
These include total boundedness, compactness, continuity and
uniform continuity. Offering concise and to-the-point treatment
of each topic in the framework of a normed space and of an inner
product space, the book represents a valuable resource for
advanced undergraduate students in mathematics, and will also
appeal to graduate students and faculty in the natural sciences
and engineering. The book is accessible to anyone who is familiar
with linear algebra and real analysis.
The entire book can be used as a textbook for an introductory
course in functional analysis without having to make any specific
selection from the topics presented here. Basic notions in the
setting of a metric space are defined in terms of sequences.
These include total boundedness, compactness, continuity and
uniform continuity. Offering concise and to-the-point treatment
of each topic in the framework of a normed space and of an inner
product space, the book represents a valuable resource for
advanced undergraduate students in mathematics, and will also
appeal to graduate students and faculty in the natural sciences
and engineering. The book is accessible to anyone who is familiar
with linear algebra and real analysis.