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This book focuses on developments in complex dynamical systems and
geometric function theory over the past decade, showing strong
links with other areas of mathematics and the natural sciences.
Traditional methods and approaches surface in physics and in the
life and engineering sciences with increasing frequency - the
Schramm-Loewner evolution, Laplacian growth, and quadratic
differentials are just a few typical examples. This book provides a
representative overview of these processes and collects open
problems in the various areas, while at the same time showing where
and how each particular topic evolves. This volume is dedicated to
the memory of Alexander Vasiliev.
This book focuses on developments in complex dynamical systems and
geometric function theory over the past decade, showing strong
links with other areas of mathematics and the natural sciences.
Traditional methods and approaches surface in physics and in the
life and engineering sciences with increasing frequency - the
Schramm-Loewner evolution, Laplacian growth, and quadratic
differentials are just a few typical examples. This book provides a
representative overview of these processes and collects open
problems in the various areas, while at the same time showing where
and how each particular topic evolves. This volume is dedicated to
the memory of Alexander Vasiliev.
Over the course of his distinguished career, Vladimir Maz'ya has
made a number of groundbreaking contributions to numerous areas of
mathematics, including partial differential equations, function
theory, and harmonic analysis. The chapters in this volume -
compiled on the occasion of his 80th birthday - are written by
distinguished mathematicians and pay tribute to his many
significant and lasting achievements.
This volume presents selected contributions from experts gathered
at Chapman University for a conference held in November 2019 on new
directions in function theory. The papers, written by leading
researchers in the field, relate to hypercomplex analysis, Schur
analysis and de Branges spaces, new aspects of classical function
theory, and infinite dimensional analysis. Signal processing
constitutes a strong presence in several of the papers.A second
volume in this series of conferences, this book will appeal to
mathematicians interested in learning about new fields of
development in function theory.
This volume presents selected contributions from experts gathered
at Chapman University for a conference held in November 2019 on new
directions in function theory. The papers, written by leading
researchers in the field, relate to hypercomplex analysis, Schur
analysis and de Branges spaces, new aspects of classical function
theory, and infinite dimensional analysis. Signal processing
constitutes a strong presence in several of the papers.A second
volume in this series of conferences, this book will appeal to
mathematicians interested in learning about new fields of
development in function theory.
This book describes recent developments as well as some classical
results regarding holomorphic mappings. The book starts with a
brief survey of the theory of semigroups of linear operators
including the Hille-Yosida and the Lumer-Phillips theorems. The
numerical range and the spectrum of closed densely defined linear
operators are then discussed in more detail and an overview of
ergodic theory is presented. The analytic extension of semigroups
of linear operators is also discussed. The recent study of the
numerical range of composition operators on the unit disk is
mentioned. Then, the basic notions and facts in infinite
dimensional holomorphy and hyperbolic geometry in Banach and
Hilbert spaces are presented, L. A. Harris' theory of the numerical
range of holomorphic mappings is generalized, and the main
properties of the so-called quasi-dissipative mappings and their
growth estimates are studied. In addition, geometric and
quantitative analytic aspects of fixed point theory are discussed.
A special chapter is devoted to applications of the numerical range
to diverse geometric and analytic problems.
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