Regular Functions of a Quaternionic Variable - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regular Functions of a Quaternionic Variable write by Graziano Gentili. This book was released on 2022-09-23. Regular Functions of a Quaternionic Variable available 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.
Regular Functions of a Quaternionic Variable
Regular Functions of a Quaternionic Variable - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regular Functions of a Quaternionic Variable write by Graziano Gentili. This book was released on 2023-09-26. Regular Functions of a Quaternionic Variable available 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.
Entire Slice Regular Functions
Entire Slice Regular Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Entire Slice Regular Functions write by Fabrizio Colombo. This book was released on 2016-12-08. Entire Slice Regular Functions available in PDF, EPUB and Kindle. This Briefs volume develops the theory of entire slice regular functions. It is the first self-contained, monographic work on the subject, offering all the necessary background information and detailed studies on several central topics, including estimates on the minimum modulus of regular functions, relations between Taylor coefficients and the growth of entire functions, density of their zeros, and the universality properties. The proofs presented here shed new light on the nature of the quaternionic setting and provide inspiration for further research directions. Also featuring an exhaustive reference list, the book offers a valuable resource for graduate students, postgraduate students and researchers in various areas of mathematical analysis, in particular hypercomplex analysis and approximation theory.
Spectral Theory on the S-Spectrum for Quaternionic Operators
Spectral Theory on the S-Spectrum for Quaternionic Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Theory on the S-Spectrum for Quaternionic Operators write by Fabrizio Colombo. This book was released on 2019-01-04. Spectral Theory on the S-Spectrum for Quaternionic Operators available 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.
Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes write by Fabrizio Colombo. This book was released on 2019-07-10. Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes available 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).
