|
Showing 1 - 5 of
5 matches in All Departments
This monograph offers an introduction to finite Blaschke products
and their connections to complex analysis, linear algebra, operator
theory, matrix analysis, and other fields. Old favorites such as
the Caratheodory approximation and the Pick interpolation theorems
are featured, as are many topics that have never received a modern
treatment, such as the Bohr radius and Ritt's theorem on
decomposability. Deep connections to hyperbolic geometry are
explored, as are the mapping properties, zeros, residues, and
critical points of finite Blaschke products. In addition, model
spaces, rational functions with real boundary values, spectral
mapping properties of the numerical range, and the Darlington
synthesis problem from electrical engineering are also covered.
Topics are carefully discussed, and numerous examples and
illustrations highlight crucial ideas. While thorough explanations
allow the reader to appreciate the beauty of the subject, relevant
exercises following each chapter improve technical fluency with the
material. With much of the material previously scattered throughout
mathematical history, this book presents a cohesive, comprehensive
and modern exposition accessible to undergraduate students,
graduate students, and researchers who have familiarity with
complex analysis.
Using a modern matrix-based approach, this rigorous second course
in linear algebra helps upper-level undergraduates in mathematics,
data science, and the physical sciences transition from basic
theory to advanced topics and applications. Its clarity of
exposition together with many illustrations, 900+ exercises, and
350 conceptual and numerical examples aid the student's
understanding. Concise chapters promote a focused progression
through essential ideas. Topics are derived and discussed in
detail, including the singular value decomposition, Jordan
canonical form, spectral theorem, QR factorization, normal
matrices, Hermitian matrices, and positive definite matrices. Each
chapter ends with a bullet list summarizing important concepts. New
to this edition are chapters on matrix norms and positive matrices,
many new sections on topics including interpolation and LU
factorization, 300+ more problems, many new examples, and
color-enhanced figures. Prerequisites include a first course in
linear algebra and basic calculus sequence. Instructor's resources
are available.
Aimed at graduate students, this textbook provides an accessible
and comprehensive introduction to operator theory. Rather than
discuss the subject in the abstract, this textbook covers the
subject through twenty examples of a wide variety of operators,
discussing the norm, spectrum, commutant, invariant subspaces, and
interesting properties of each operator. The text is supplemented
by over 600 end-of-chapter exercises, designed to help the reader
master the topics covered in the chapter, as well as providing an
opportunity to further explore the vast operator theory literature.
Each chapter also contains well-researched historical facts which
place each chapter within the broader context of the development of
the field as a whole.
Aimed at graduate students, this textbook provides an accessible
and comprehensive introduction to operator theory. Rather than
discuss the subject in the abstract, this textbook covers the
subject through twenty examples of a wide variety of operators,
discussing the norm, spectrum, commutant, invariant subspaces, and
interesting properties of each operator. The text is supplemented
by over 600 end-of-chapter exercises, designed to help the reader
master the topics covered in the chapter, as well as providing an
opportunity to further explore the vast operator theory literature.
Each chapter also contains well-researched historical facts which
place each chapter within the broader context of the development of
the field as a whole.
The study of model spaces, the closed invariant subspaces of the
backward shift operator, is a vast area of research with
connections to complex analysis, operator theory and functional
analysis. This self-contained text is the ideal introduction for
newcomers to the field. It sets out the basic ideas and quickly
takes the reader through the history of the subject before ending
up at the frontier of mathematical analysis. Open questions point
to potential areas of future research, offering plenty of
inspiration to graduate students wishing to advance further.
|
|