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Finite Blaschke Products and Their Connections
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 Darlingt...
The Cauchy Transform
The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.
Generalized Analytic Continuation
The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. They are careful to cover the various types of continuations, attempting to unify them and suggesting some open questions. The book also addresses the role of such continuations in approximation theory and operator theory. The introductory overview provides a useful look at the history and context of the theory.
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To Change the Church
A New York Times columnist and one of America’s leading conservative thinkers considers Pope Francis’s efforts to change the church he governs in a book that is “must reading for every Christian who cares about the fate of the West and the future of global Christianity” (Rod Dreher, author of The Benedict Option). Born Jorge Mario Bergoglio in 1936, today Pope Francis is the 266th pope of the Roman Catholic Church. Pope Francis’s stewardship of the Church, while perceived as a revelation by many, has provoked division throughout the world. “If a conclave were to be held today,” one Roman source told The New Yorker, “Francis would be lucky to get ten votes.” In his “concis...
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