Quaternionic Approximation
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Quaternionic Approximation
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Author : Sorin G. Gal
language : en
Publisher: Springer
Release Date : 2019-04-12
Quaternionic Approximation written by Sorin G. Gal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-12 with Mathematics categories.
This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable. The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.
Quaternionic Quantum Mechanics And Quantum Fields
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Author : Stephen L. Adler
language : en
Publisher: Oxford University Press
Release Date : 1995-04-27
Quaternionic Quantum Mechanics And Quantum Fields written by Stephen L. Adler and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Science categories.
It has been known since the 1930s that quantum mechanics can be formulated in quaternionic as well as complex Hilbert space. But systematic work on the quaternionic extension of standard quantum mechanics has scarcely begun. Authored by a world-renowned theoretical physicist, this book signals a major conceptual advance and gives a detailed development and exposition of quaternionic quantum mechanics for the purpose of determining whether quaternionic Hilbert space is the appropriate arena for the long sought-after unification of the standard model forces with gravitation. Significant results from earlier literature, together with many new results obtained by the author, are integrated to give a coherent picture of the subject. The book also provides an introduction to the problem of formulating quantum field theories in quaternionic Hilbert space. The book concludes with a chapter devoted to discussions on where quaternionic quantum mechanics may fit into the physics of unification, experimental and measurement theory issues, and the many open questions that still challenge the field. This well-written treatise is a very significant contribution to theoretical physics. It will be eagerly read by a wide range of physicists.
Quaternionic Integral Transforms
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Author : Eckhard Hitzer
language : en
Publisher: Springer Nature
Release Date : 2023-08-08
Quaternionic Integral Transforms written by Eckhard Hitzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-08 with Mathematics categories.
This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Quaternionic Closed Operators Fractional Powers And Fractional Diffusion Processes
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Author : Fabrizio Colombo
language : en
Publisher: Springer
Release Date : 2019-07-10
Quaternionic Closed Operators Fractional Powers And Fractional Diffusion Processes written by Fabrizio Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-10 with Mathematics categories.
This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields. This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey (Operator Theory: Advances and Applications, Vol. 270).
Regular Functions Of A Quaternionic Variable
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Author : Graziano Gentili
language : en
Publisher: Springer Nature
Release Date : 2022-09-23
Regular Functions Of A Quaternionic Variable written by Graziano Gentili and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-23 with Mathematics categories.
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions
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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2024-12-09
Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-09 with Mathematics categories.
The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.
Spectral Theory On The S Spectrum For Quaternionic Operators
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Author : Fabrizio Colombo
language : en
Publisher: Springer
Release Date : 2019-01-04
Spectral Theory On The S Spectrum For Quaternionic Operators written by Fabrizio Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-04 with Mathematics categories.
The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.
Quaternion Algebras
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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Guide To Geometric Algebra In Practice
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Author : Leo Dorst
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-28
Guide To Geometric Algebra In Practice written by Leo Dorst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-28 with Mathematics categories.
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
Progress In Pattern Recognition Image Analysis And Applications
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Author : Alberto Sanfeliu
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-15
Progress In Pattern Recognition Image Analysis And Applications written by Alberto Sanfeliu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-15 with Computers categories.
First of all, we want to congratulate two new research communities from M- ico and Brazil that have recently joined the Iberoamerican community and the International Association for Pattern Recognition. We believe that the series of congresses that started as the “Taller Iberoamericano de Reconocimiento de Patrones (TIARP)”, and later became the “Iberoamerican Congress on Pattern Recognition (CIARP)”, has contributed to these groupconsolidatione?orts. We hope that in the near future all the Iberoamerican countries will have their own groups and associations to promote our areas of interest; and that these congresses will serve as the forum for scienti?c research exchange, sharing of - pertise and new knowledge, and establishing contacts that improve cooperation between research groups in pattern recognition and related areas. CIARP 2004 (9th Iberoamerican Congress on Pattern Recognition) was the ninthinaseriesofpioneeringcongressesonpatternrecognitionintheIberoam- ican community. As in the previous year, CIARP 2004 also included worldwide participation. It took place in Puebla, Mexico. The aim of the congress was to promote and disseminate ongoing research and mathematical methods for pattern recognition, image analysis, and applications in such diverse areas as computer vision, robotics, industry, health, entertainment, space exploration, telecommunications, data mining, document analysis,and natural languagep- cessing and recognition, to name a few.