This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.
A set V in a domain U in Cn has the norm-preserving extension property if every bounded holomorphic function on V has a holomorphic extension to U with the same supremum norm. We prove that an algebraic subset of the symmetrized bidisc
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
This work begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains. The generalized Herglotz kernels that appear in these representation theorems are then exploited to evolve new conditions for spectral set and rational dilation conditions over multiply-connected domains. These conditions form the basis for the theoretical development of a computational procedure for probing a well-known unsolved problem in operator theory, the so called rational dilation conjecture. Arbitrary precision algorithms for computing the Herglotz kernels on circled domains are presented and analyzed. These algorithms permit an effective implementation of the computational procedure which results in a machine generated counterexample to the rational dilation conjecture.
Rutter’s Child and Adolescent Psychiatry has become an established and accepted textbook of child psychiatry. Now completely revised and updated, the fifth edition provides a coherent appraisal of the current state of the field to help trainee and practising clinicians in their daily work. It is distinctive in being both interdisciplinary and international, in its integration of science and clinical practice, and in its practical discussion of how researchers and practitioners need to think about conflicting or uncertain findings. This new edition now offers an entirely new section on conceptual approaches, and several new chapters, including: neurochemistry and basic pharmacology brain imaging health economics psychopathology in refugees and asylum seekers bipolar disorder attachment disorders statistical methods for clinicians This leading textbook provides an accurate and comprehensive account of current knowledge, through the integration of empirical findings with clinical experience and practice, and is essential reading for professionals working in the field of child and adolescent mental health, and clinicians working in general practice and community pediatric settings.
In the 1880s, a Brooklyn baseball manager plotted to steal pitching signs and alert batters with a hidden electrical wire. In 1951, the Brooklyn Dodgers were robbed of a pennant via a sign-stealing scheme involving a center field office, a telescope and a button connected to the bullpen phone. In 2017, the Los Angeles Dodgers were robbed of a World Series championship via a sign-stealing system involving a TV camera, a monitor, a trash can and a bat. History has often repeated itself around the Dodgers franchise. From their beginnings as the Brooklyn Atlantics to their move from Flatbush to L.A. and into the 21st Century, the Dodgers have seen heartbreaking losses and stirring triumphs, broken the color barrier, turned the game into a true coast-to-coast sport and produced many Hall of Famers, This is their story.
This title tells the story of the Women's National Basketball Association, from its founding in the 1990s to its status today as a world-class showcase for basketball talent. Readers will learn about the league's stars, teams, and coaches, as well as player efforts to earn higher pay. Features include infographics, a glossary, references, websites, source notes, and an index. Aligned to Common Core Standards and correlated to state standards. Essential Library is an imprint of Abdo Publishing, a division of ABDO.
For nearly a century Columbus, Ohio pizza parlors have served up delicious meals by the tray and by the slice. This history goes back to the 1930s, when TAT Ristorante began serving pizza. Today, it is the oldest family-owned restaurant in the city. Over the years, a specific style evolved guided by the experiences and culinary interpretations of local pizza pioneers like Jimmy Massey, Romeo Sirij, Tommy Iacono, Joe Gatto, Cosmo Leonardo, Pat Orecchio, Reuben Cohen, Guido Casa and Richie DiPaolo. The years of experimentation and refinement culminated in Columbus being crowned the pizza capital of the USA in the 1990s. Author and founder of the city's first pizza tour Jim Ellison chronicles one of the city's favorite foods.
This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.
A set V in a domain U in Cn has the norm-preserving extension property if every bounded holomorphic function on V has a holomorphic extension to U with the same supremum norm. We prove that an algebraic subset of the symmetrized bidisc
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^\infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^\infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
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