Spectral Theory On The S Spectrum For Quaternionic Operators
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| Author | : Fabrizio Colombo |
| Publisher | : Springer |
| Total Pages | : 356 |
| Release | : 2019-01-04 |
| Genre | : Mathematics |
| ISBN | : 3030030741 |
Download Spectral Theory on the S-Spectrum for Quaternionic Operators Book in PDF, Epub and Kindle
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.
| Author | : Fabrizio Colombo |
| Publisher | : Springer |
| Total Pages | : 322 |
| Release | : 2019-07-10 |
| Genre | : Mathematics |
| ISBN | : 3030164098 |
Download Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes Book in PDF, Epub and Kindle
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).
| Author | : Jonathan Gantner |
| Publisher | : American Mathematical Society |
| Total Pages | : 114 |
| Release | : 2021-02-10 |
| Genre | : Mathematics |
| ISBN | : 1470442388 |
Download Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators Book in PDF, Epub and Kindle
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
| Author | : Fabrizio Colombo |
| Publisher | : Springer Nature |
| Total Pages | : 126 |
| Release | : 2020-10-24 |
| Genre | : Mathematics |
| ISBN | : 3030502163 |
Download Michele Sce's Works in Hypercomplex Analysis Book in PDF, Epub and Kindle
This book presents English translations of Michele Sce’s most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality. This volume is dedicated to revealing and describing the framework Sce worked in, at an exciting time when the various generalizations of complex analysis in one variable were still in their infancy. In addition to faithfully translating Sce’s papers, the authors discuss their significance and explain their connections to contemporary research in hypercomplex analysis. They also discuss many concrete examples that can serve as a basis for further research. The vast majority of the results presented here will be new to readers, allowing them to finally access the original sources with the benefit of comments from fellow mathematicians active in the field of hypercomplex analysis. As such, the book offers not only an important chapter in the history of hypercomplex analysis, but also a roadmap for further exciting research in the field.
| Author | : David Edmunds |
| Publisher | : Oxford University Press |
| Total Pages | : |
| Release | : 2018-05-03 |
| Genre | : Mathematics |
| ISBN | : 0192540106 |
Download Spectral Theory and Differential Operators Book in PDF, Epub and Kindle
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
| Author | : Andrei Giniatoulline |
| Publisher | : R.T. Edwards, Inc. |
| Total Pages | : 212 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9781930217096 |
Download An Introduction to Spectral Theory Book in PDF, Epub and Kindle
A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.
| Author | : K. B. Laursen |
| Publisher | : Oxford University Press |
| Total Pages | : 610 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780198523819 |
Download An Introduction to Local Spectral Theory Book in PDF, Epub and Kindle
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
| Author | : Jonathan Gantner |
| Publisher | : American Mathematical Society |
| Total Pages | : 114 |
| Release | : 2021-02-10 |
| Genre | : Mathematics |
| ISBN | : 1470442388 |
Download Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators Book in PDF, Epub and Kindle
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
| Author | : Vladimir Müller |
| Publisher | : Birkhäuser |
| Total Pages | : 390 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 3034877889 |
Download Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras Book in PDF, Epub and Kindle
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
| Author | : William Arveson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 143 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387215182 |
Download A Short Course on Spectral Theory Book in PDF, Epub and Kindle
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.
