Dirichlet Series and Holomorphic Functions in High Dimensions PDF Download
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Author: Andreas Defant
Publisher: Cambridge University Press
ISBN: 1108476716
Category : Mathematics
Languages : en
Pages : 709
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Book Description
Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Author: Andreas Defant
Publisher: Cambridge University Press
ISBN: 1108476716
Category : Mathematics
Languages : en
Pages : 709
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Book Description
Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Author: Klaus Gürlebeck
Publisher: Springer
ISBN: 3034809646
Category : Mathematics
Languages : en
Pages : 390
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Book Description
This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
Author: Klaus Gürlebeck
Publisher: Springer Science & Business Media
ISBN: 3764382716
Category : Mathematics
Languages : en
Pages : 407
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Book Description
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.
Author: Hervé Queffélec
Publisher: Springer Nature
ISBN: 9811593515
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition operators, and connections between these two domains which often occur through the Kronecker approximation theorem and the Bohr lift. The book initially discusses Harmonic analysis, including a sharp form of the uncertainty principle, Ergodic theory and Diophantine approximation, basics on continued fractions expansions, and the mixing property of the Gauss map and goes on to present the general theory of Dirichlet series with classes of examples connected to continued fractions, Bohr lift, sharp forms of the Bohnenblust–Hille theorem, Hardy–Dirichlet spaces, composition operators of the Hardy–Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory, and ergodic theory, featuring the richness of analytic theory of Dirichlet series. This self-contained book benefits beginners as well as researchers.
Author: José Bonet
Publisher: Springer Nature
ISBN: 3031416023
Category : Mathematics
Languages : en
Pages : 279
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Book Description
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.
Author: Tasho Kaletha
Publisher: Cambridge University Press
ISBN: 1108935028
Category : Mathematics
Languages : en
Pages : 750
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Book Description
Bruhat-Tits theory that suffices for the main applications. Part III treats modern topics that have become important in current research. Part IV provides a few sample applications of the theory. The appendices contain further details on the topic of integral models.
Author: Joachim Schwermer
Publisher: Cambridge University Press
ISBN: 1108935079
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures and they arise in many areas of study. This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number theoretical components to the investigations of arithmetic groups, and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces, and some associated cohomological questions. Written by a renowned expert, this book is a valuable reference for researchers and graduate students.
Author: Janina Kotus
Publisher: Cambridge University Press
ISBN: 1009215914
Category : Mathematics
Languages : en
Pages : 509
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Book Description
A comprehensive and detailed presentation of finite and infinite ergodic theory, fractal measures, and thermodynamic formalism.
Author: Janina Kotus
Publisher: Cambridge University Press
ISBN: 1009215906
Category : Mathematics
Languages : en
Pages : 510
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Book Description
This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students.
Author: Paul F. X. Müller
Publisher: Cambridge University Press
ISBN: 1108985963
Category : Mathematics
Languages : en
Pages :
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Book Description
This book presents the probabilistic methods around Hardy martingales for an audience interested in their applications to complex, harmonic, and functional analysis. Building on work of Bourgain, Garling, Jones, Maurey, Pisier, and Varopoulos, it discusses in detail those martingale spaces that reflect characteristic qualities of complex analytic functions. Its particular themes are holomorphic random variables on Wiener space, and Hardy martingales on the infinite torus product, and numerous deep applications to the geometry and classification of complex Banach spaces, e.g., the SL∞ estimates for Doob's projection operator, the embedding of L1 into L1/H1, the isomorphic classification theorem for the polydisk algebras, or the real variables characterization of Banach spaces with the analytic Radon Nikodym property. Due to the inclusion of key background material on stochastic analysis and Banach space theory, it's suitable for a wide spectrum of researchers and graduate students working in classical and functional analysis.
