Quaternionic Closed Operators Fractional Powers And Fractional Diffusion Processes PDF Download
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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 | : 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 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 | : Sorin G. Gal |
Publisher | : Springer |
Total Pages | : 221 |
Release | : 2019-04-12 |
Genre | : Mathematics |
ISBN | : 3030106667 |
Download Quaternionic Approximation Book in PDF, ePub and Kindle
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.
Author | : Graziano Gentili |
Publisher | : Springer Nature |
Total Pages | : 302 |
Release | : 2022-09-23 |
Genre | : Mathematics |
ISBN | : 3031075315 |
Download Regular Functions of a Quaternionic Variable Book in PDF, ePub and Kindle
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.
Author | : Daniel Alpay |
Publisher | : Springer Nature |
Total Pages | : 424 |
Release | : 2023-04-11 |
Genre | : Mathematics |
ISBN | : 3031214609 |
Download Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis Book in PDF, ePub and Kindle
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
Author | : Fabrizio Colombo |
Publisher | : Birkhäuser |
Total Pages | : 398 |
Release | : 2017-09-30 |
Genre | : Mathematics |
ISBN | : 3319623621 |
Download Advances in Complex Analysis and Operator Theory Book in PDF, ePub and Kindle
This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.
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 | : Daniel Alpay |
Publisher | : Springer Nature |
Total Pages | : 121 |
Release | : 2020-01-27 |
Genre | : Mathematics |
ISBN | : 3030383121 |
Download Quaternionic de Branges Spaces and Characteristic Operator Function Book in PDF, ePub and Kindle
This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
Author | : Swanhild Bernstein |
Publisher | : Springer |
Total Pages | : 228 |
Release | : 2014-10-10 |
Genre | : Mathematics |
ISBN | : 3319087711 |
Download Hypercomplex Analysis: New Perspectives and Applications Book in PDF, ePub and Kindle
Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.