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The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.
Book Synopsis Continuous Semigroups of Holomorphic Self-maps of the Unit Disc by : Filippo Bracci
Download or read book Continuous Semigroups of Holomorphic Self-maps of the Unit Disc written by Filippo Bracci and published by Springer Nature. This book was released on 2020-02-14 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.
This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.
Book Synopsis Holomorphic Dynamics on Hyperbolic Riemann Surfaces by : Marco Abate
Download or read book Holomorphic Dynamics on Hyperbolic Riemann Surfaces written by Marco Abate and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-12-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.
This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.
Book Synopsis Complex Analysis and Dynamical Systems VI by : Lawrence Zalcman
Download or read book Complex Analysis and Dynamical Systems VI written by Lawrence Zalcman and published by American Mathematical Soc.. This book was released on 2016-05-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.
The aim of this work is to present, in a unified and reasonably self-contained way, certain aspects of functional analysis which are needed to treat function spaces whose topology is not derived from a single norm, their topological duals and operators between those spaces. We treat spaces of continuous, analytic and smooth functions as well as sequence spaces. Operators of differentiation, integration, composition, multiplication and partial differential operators between those spaces are studied. A brief introduction to Laurent Schwartz’s theory of distributions and to Lars Hörmander’s approach to linear partial differential operators is presented. The novelty of our approach lies mainly on two facts. First of all, we show all these topics together in an accessible way, stressing the connection between them. Second, we keep it always at a level that is accessible to beginners and young researchers. Moreover, parts of the book might be of interest for researchers in functional analysis and operator theory. Our aim is not to build and describe a whole, complete theory, but to serve as an introduction to some aspects that we believe are interesting. We wish to guide any reader that wishes to enter in some of these topics in their first steps. Our hope is that they learn interesting aspects of functional analysis and become interested to broaden their knowledge about function and sequence spaces and operators between them. The text is addressed to students at a master level, or even undergraduate at the last semesters, since only knowledge on real and complex analysis is assumed. We have intended to be as self-contained as possible, and wherever an external citation is needed, we try to be as precise as we can. Our aim is to be an introduction to topics in, or connected with, different aspects of functional analysis. Many of them are in some sense classical, but we tried to show a unified direct approach; some others are new. This is why parts of these lectures might be of some interest even for researchers in related areas of functional analysis or operator theory. There is a full chapter about transitive and mean ergodic operators on locally convex spaces. This material is new in book form. It is a novel approach and can be of interest for researchers in the area.
Book Synopsis Function Spaces and Operators between them by : José Bonet
Download or read book Function Spaces and Operators between them written by José Bonet and published by Springer Nature. This book was released on 2023-11-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to present, in a unified and reasonably self-contained way, certain aspects of functional analysis which are needed to treat function spaces whose topology is not derived from a single norm, their topological duals and operators between those spaces. We treat spaces of continuous, analytic and smooth functions as well as sequence spaces. Operators of differentiation, integration, composition, multiplication and partial differential operators between those spaces are studied. A brief introduction to Laurent Schwartz’s theory of distributions and to Lars Hörmander’s approach to linear partial differential operators is presented. The novelty of our approach lies mainly on two facts. First of all, we show all these topics together in an accessible way, stressing the connection between them. Second, we keep it always at a level that is accessible to beginners and young researchers. Moreover, parts of the book might be of interest for researchers in functional analysis and operator theory. Our aim is not to build and describe a whole, complete theory, but to serve as an introduction to some aspects that we believe are interesting. We wish to guide any reader that wishes to enter in some of these topics in their first steps. Our hope is that they learn interesting aspects of functional analysis and become interested to broaden their knowledge about function and sequence spaces and operators between them. The text is addressed to students at a master level, or even undergraduate at the last semesters, since only knowledge on real and complex analysis is assumed. We have intended to be as self-contained as possible, and wherever an external citation is needed, we try to be as precise as we can. Our aim is to be an introduction to topics in, or connected with, different aspects of functional analysis. Many of them are in some sense classical, but we tried to show a unified direct approach; some others are new. This is why parts of these lectures might be of some interest even for researchers in related areas of functional analysis or operator theory. There is a full chapter about transitive and mean ergodic operators on locally convex spaces. This material is new in book form. It is a novel approach and can be of interest for researchers in the area.
The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.
Book Synopsis Early Days in Complex Dynamics by : Daniel S. Alexander
Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander and published by American Mathematical Soc.. This book was released on 2012 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.
This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.
Book Synopsis Harmonic and Complex Analysis and its Applications by : Alexander Vasil'ev
Download or read book Harmonic and Complex Analysis and its Applications written by Alexander Vasil'ev and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.
This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on "Composition Operators on Spaces of Analytic Functions" held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.
Book Synopsis Studies on Composition Operators by : Rocky Mountain Mathematics Consortium
Download or read book Studies on Composition Operators written by Rocky Mountain Mathematics Consortium and published by American Mathematical Soc.. This book was released on 1998 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on "Composition Operators on Spaces of Analytic Functions" held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.
Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces. This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
Book Synopsis Linearization Models for Complex Dynamical Systems by : Mark Elin
Download or read book Linearization Models for Complex Dynamical Systems written by Mark Elin and published by Springer Science & Business Media. This book was released on 2011-02-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces. This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
