Geometric Analysis Of The Bergman Kernel And Metric

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Geometric Analysis of the Bergman Kernel and Metric

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
ISBN 13 : 146147924X
Total Pages : 300 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Geometric Analysis of the Bergman Kernel and Metric by : Steven G. Krantz

Download or read book Geometric Analysis of the Bergman Kernel and Metric written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.

Geometric Analysis and Function Spaces

Author : Steven George Krantz
Publisher : American Mathematical Soc.
ISBN 13 : 082180734X
Total Pages : 216 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Analysis and Function Spaces by : Steven George Krantz

Download or read book Geometric Analysis and Function Spaces written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 1993 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Handbook of Complex Analysis

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1351663054
Total Pages : 519 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Complex Analysis by : Steven G. Krantz

Download or read book Handbook of Complex Analysis written by Steven G. Krantz and published by CRC Press. This book was released on 2022-03-07 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. This book is also a reference and a source of inspiration for more seasoned mathematicians—both specialists in complex analysis and others who want to acquaint themselves with current modes of thought. The chapters in this volume are authored by leading experts and gifted expositors. They are carefully crafted presentations of diverse aspects of the field, formulated for a broad and diverse audience. This volume is a touchstone for current ideas in the broadly construed subject area of complex analysis. It should enrich the literature and point in some new directions.

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

Author : Palle Jorgensen
Publisher : World Scientific
ISBN 13 : 9811225796
Total Pages : 253 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by : Palle Jorgensen

Download or read book Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory written by Palle Jorgensen and published by World Scientific. This book was released on 2021-01-15 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Geometric Analysis of PDEs and Several Complex Variables

Author : Shiferaw Berhanu
Publisher : Springer Nature
ISBN 13 : 3031697022
Total Pages : 357 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Geometric Analysis of PDEs and Several Complex Variables by : Shiferaw Berhanu

Download or read book Geometric Analysis of PDEs and Several Complex Variables written by Shiferaw Berhanu and published by Springer Nature. This book was released on with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Complex Analysis

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470411016
Total Pages : 339 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Advanced Complex Analysis by : Barry Simon

Download or read book Advanced Complex Analysis written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2B provides a comprehensive look at a number of subjects of complex analysis not included in Part 2A. Presented in this volume are the theory of conformal metrics (including the Poincaré metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painlevé smoothness theorem), topics in analytic number theory (including Jacobi's two- and four-square theorems, the Dirichlet prime progression theorem, the prime number theorem, and the Hardy-Littlewood asymptotics for the number of partitions), the theory of Fuschian differential equations, asymptotic methods (including Euler's method, stationary phase, the saddle-point method, and the WKB method), univalent functions (including an introduction to SLE), and Nevanlinna theory. The chapters on Fuschian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.

Geometric Complex Analysis

Author : Jisoo Byun
Publisher : Springer
ISBN 13 : 9811316724
Total Pages : 359 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Geometric Complex Analysis by : Jisoo Byun

Download or read book Geometric Complex Analysis written by Jisoo Byun and published by Springer. This book was released on 2018-09-08 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.

The Dirichlet Space and Related Function Spaces

Author : Nicola Arcozzi
Publisher : American Mathematical Soc.
ISBN 13 : 1470450828
Total Pages : 559 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Dirichlet Space and Related Function Spaces by : Nicola Arcozzi

Download or read book The Dirichlet Space and Related Function Spaces written by Nicola Arcozzi and published by American Mathematical Soc.. This book was released on 2019-09-03 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

Differential Geometry and Analysis on CR Manifolds

Author : Sorin Dragomir
Publisher : Springer Science & Business Media
ISBN 13 : 0817644830
Total Pages : 499 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Differential Geometry and Analysis on CR Manifolds by : Sorin Dragomir

Download or read book Differential Geometry and Analysis on CR Manifolds written by Sorin Dragomir and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study

Analysis Meets Geometry

Author : Mats Andersson
Publisher : Birkhäuser
ISBN 13 : 3319524712
Total Pages : 464 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Analysis Meets Geometry by : Mats Andersson

Download or read book Analysis Meets Geometry written by Mats Andersson and published by Birkhäuser. This book was released on 2017-09-04 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

Issues in Algebra, Geometry, and Topology: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490108440
Total Pages : 687 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Algebra, Geometry, and Topology: 2013 Edition by :

Download or read book Issues in Algebra, Geometry, and Topology: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Analysis, Complex Geometry, and Mathematical Physics

Author : Paul M. N. Feehan
Publisher : American Mathematical Soc.
ISBN 13 : 1470414643
Total Pages : 388 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analysis, Complex Geometry, and Mathematical Physics by : Paul M. N. Feehan

Download or read book Analysis, Complex Geometry, and Mathematical Physics written by Paul M. N. Feehan and published by American Mathematical Soc.. This book was released on 2015-07-21 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.

The Bergman Kernel and Related Topics

Author : Kengo Hirachi
Publisher : Springer Nature
ISBN 13 : 981999506X
Total Pages : 372 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis The Bergman Kernel and Related Topics by : Kengo Hirachi

Download or read book The Bergman Kernel and Related Topics written by Kengo Hirachi and published by Springer Nature. This book was released on with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Geometric Analysis in Pohang

Author : Kang-Tae Kim
Publisher : American Mathematical Soc.
ISBN 13 : 0821809571
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Geometric Analysis in Pohang by : Kang-Tae Kim

Download or read book Complex Geometric Analysis in Pohang written by Kang-Tae Kim and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of a conference on the geometric analysis of several complex variables held at POSTECH in June 1997. The conference was attended by scienctists and students from around the globe. Each of the five plenary speakers at the conference gave a short course on a topic of current interest in the field. The lecture write-ups contain cogent and accessible information intended for a broad audience. The volume also includes a tutorial in several complex variables given by Kim and Krantz at the conference. This tutorial is geared toward helping the novice to understand the rest of the material in the book. The bibliographies of the papers give students and young mathematicians a valuable resource for future learning on the topic. This book provides a substantial overview on areas of current activity. Required background for understanding the text is a solid undergraduate education in mathematics and familiarity with first year graduate studies in real and complex analysis. Some exposure to geometry would be helpful. The book is also suitable for use as a supplemental course text.

Geometric Analysis of PDE and Several Complex Variables

Author : Francois Treves
Publisher : American Mathematical Soc.
ISBN 13 : 0821833863
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Analysis of PDE and Several Complex Variables by : Francois Treves

Download or read book Geometric Analysis of PDE and Several Complex Variables written by Francois Treves and published by American Mathematical Soc.. This book was released on 2005 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.

Harmonic and Complex Analysis in Several Variables

Author : Steven G. Krantz
Publisher : Springer
ISBN 13 : 3319632310
Total Pages : 429 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Harmonic and Complex Analysis in Several Variables by : Steven G. Krantz

Download or read book Harmonic and Complex Analysis in Several Variables written by Steven G. Krantz and published by Springer. This book was released on 2017-09-20 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

The Geometry of Complex Domains

Author : Robert E. Greene
Publisher : Springer Science & Business Media
ISBN 13 : 0817646221
Total Pages : 310 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Geometry of Complex Domains by : Robert E. Greene

Download or read book The Geometry of Complex Domains written by Robert E. Greene and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.