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Holomorphic Spaces
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Book Synopsis Holomorphic Spaces by : Sheldon Jay Axler
Download or read book Holomorphic Spaces written by Sheldon Jay Axler and published by Cambridge University Press. This book was released on 1998-05-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
Book Synopsis Spaces of Holomorphic Functions in the Unit Ball by : Kehe Zhu
Download or read book Spaces of Holomorphic Functions in the Unit Ball written by Kehe Zhu and published by Springer Science & Business Media. This book was released on 2006-03-22 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can be used as a graduate text Contains many exercises Contains new results
Book Synopsis Holomorphic Functions in the Plane and n-dimensional Space by : Klaus Gürlebeck
Download or read book Holomorphic Functions in the Plane and n-dimensional Space written by Klaus Gürlebeck and published by Springer Science & Business Media. This book was released on 2007-11-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
Book Synopsis Introduction to the Theory of Analytic Spaces by : Raghavan Narasimhan
Download or read book Introduction to the Theory of Analytic Spaces written by Raghavan Narasimhan and published by Springer. This book was released on 2006-11-14 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Holomorphic Functions of Several Variables by : Ludger Kaup
Download or read book Holomorphic Functions of Several Variables written by Ludger Kaup and published by Walter de Gruyter. This book was released on 2011-05-09 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Book Synopsis Holomorphic Automorphism Groups in Banach Spaces by : J.M. Isidro
Download or read book Holomorphic Automorphism Groups in Banach Spaces written by J.M. Isidro and published by Elsevier. This book was released on 2011-08-18 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holomorphic Automorphism Groups in Banach Spaces
Book Synopsis Lectures on Analytic Function Spaces and their Applications by : Javad Mashreghi
Download or read book Lectures on Analytic Function Spaces and their Applications written by Javad Mashreghi and published by Springer Nature. This book was released on 2023-11-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.
Book Synopsis On the Topology of Isolated Singularities in Analytic Spaces by : José Seade
Download or read book On the Topology of Isolated Singularities in Analytic Spaces written by José Seade and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.
Book Synopsis Hyperbolic Manifolds and Holomorphic Mappings by : Shoshichi Kobayashi
Download or read book Hyperbolic Manifolds and Holomorphic Mappings written by Shoshichi Kobayashi and published by World Scientific. This book was released on 2005 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections ?invariant metrics and pseudo-distances? and ?hyperbolic complex manifolds? within the section ?holomorphic mappings?. The invariant distance introduced in the first edition is now called the ?Kobayashi distance?, and the hyperbolicity in the sense of this book is called the ?Kobayashi hyperbolicity? to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Book Synopsis Complex Analytic Desingularization by : José Manuel Aroca
Download or read book Complex Analytic Desingularization written by José Manuel Aroca and published by Springer. This book was released on 2018-11-03 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: [From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.
Download or read book Holomorphic Q Classes written by Jie Xiao and published by Springer. This book was released on 2003-07-01 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: The space Q p consists of all holomorphic functions f on the unit disk for which the L^2 area integrals of its derivative against the p-th power of the Green function of the unit disk are uniformly bounded in the variable that survives the integration. It turns out that Q 1 coincides with BMOA, while, for p>1, Q p are just the Bloch space. For p/in (0,1) the Q p furnish an increasing sequence of spaces, each invariant under conformal mappings of the unit disk onto itself, which interpolate between the Dirichlet space and BMOA. This monograph covers a number of important aspects in complex, functional and harmonic analysis. The primary focus is Q p, p/in (0,1), and their equivalent characterizations. Based on the up-to-date results obtained by experts in their respective fields, each of the eight chapters unfolds from the basics to the more complex. The exposition here is rapid-paced and efficient, with proofs and examples.
Book Synopsis Dirichlet Series and Holomorphic Functions in High Dimensions by : Andreas Defant
Download or read book Dirichlet Series and Holomorphic Functions in High Dimensions written by Andreas Defant and published by Cambridge University Press. This book was released on 2019-08-08 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Book Synopsis Holomorphic Morse Inequalities and Bergman Kernels by : Xiaonan Ma
Download or read book Holomorphic Morse Inequalities and Bergman Kernels written by Xiaonan Ma and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Book Synopsis Stein Manifolds and Holomorphic Mappings by : Franc Forstnerič
Download or read book Stein Manifolds and Holomorphic Mappings written by Franc Forstnerič and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.
Book Synopsis Hyperbolic Complex Spaces by : Shoshichi Kobayashi
Download or read book Hyperbolic Complex Spaces written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.
Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler
Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Soc.. This book was released on 2002 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $Hinfty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $Hinfty$ 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 theinterpolation 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.
Book Synopsis Function Spaces by : Krzysztof Jarosz
Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.
