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9781470472467 Academic Inspection Copy

Recent Progress in Function Theory and Operator Theory

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This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or ""models"", the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.
Alberto Condori, Florida Gulf Coast University, Fort Meyers, FL. Elodie Pozzi, St. Louis University, MO. William T. Ross, University of Richmond, VA. Alan A. Sola, Stockholm University, Sweden.
Articles Pamela Gorkin and Elodie Pozzi, Three open problems in function theoretic operator theory Dmitry Khavinson, Erik Lundberg and Sean Perry, On the valence of logharmonic polynomials Michael R. Pilla, A generalized cross ratio Zhenghui Huo and Brett D. Wick, Weighted estimates of the Bergman projection with matrix weights Galia Dafni and Chun Ho Lau, $h^1$ boundedness of localized operators and commutators with bmo and lmo Raymond Cheng and Christopher Felder, On interpolation by functions in $\ell _A^p$ Pierre-Olivier Parise, Kernel-summability methods and the Silverman-Toeplitz Theorem George Popescu and Gabriel T. Prajitura, On Rhaly operators on $l^2$ William T. Ross, The Cesaro operator
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