William T. Ross Bücher

Focusing on operator theory, this textbook is designed for graduate students and offers a clear introduction to the subject. It features twenty examples of operators, exploring key concepts such as norm, spectrum, commutant, and invariant subspaces. Each operator is examined in detail, highlighting its unique properties and applications, making it a valuable resource for those looking to deepen their understanding of this mathematical field.

This textbook serves as an accessible introduction to a complex field, making it suitable for newcomers. It not only covers foundational concepts but also highlights potential areas for future research, encouraging further exploration and study.

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 Carathéodory 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.