* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

Analysis of Dirac Systems and Computational Algebra (Progress in Mathematical Physics, 39)

Science & Math

Struppa, Daniele C.

Colombo, Fabrizio

Sabadini, Irene

Sommen, Franciscus

Mathematics

Birkhauser

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

Analysis of Dirac Systems and Computational Algebra (Progress in Mathematical Physics)

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 Approximation: With Application to Slice Regular Functions (Frontiers in Mathematics)

Gal, Sorin G.

Quaternionic de Branges Spaces and Characteristic Operator Function (SpringerBriefs in Mathematics)

Alpay, Daniel

Springer

Michele Sce's Works in Hypercomplex Analysis: A Translation with Commentaries

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,&nbsp;the authors discuss&nbsp;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&nbsp;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.

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions (Operator Theory: Advances and Applications, 304)

Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions (Progress in Mathematics, 289)

This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions.
Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.

Politecnico di Milano, Prof. Fabrizio Colombo

This exposition of the new functional calculus methodology, as well as its analog for quaternionic linear operators is informed by the recently developed theory of hyperholomorphicity and is ideal for application to n-tuples of non-commuting linear operators.

This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.

Slice Hyperholomorphic Schur Analysis (Operator Theory: Advances and Applications, 256)

See the best price to sell, buy, or rent books by Sabadini, Irene. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Sabadini, Irene

See the best price to sell, buy, or rent books by Sabadini, Irene. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Analysis of Dirac Systems and Computational Algebra (Progress in Mathematical Physics, 39)

Analysis of Dirac Systems and Computational Algebra (Progress in Mathematical Physics)

Quaternionic Approximation: With Application to Slice Regular Functions (Frontiers in Mathematics)

Quaternionic de Branges Spaces and Characteristic Operator Function (SpringerBriefs in Mathematics)

Michele Sce's Works in Hypercomplex Analysis: A Translation with Commentaries

Michele Sce's Works in Hypercomplex Analysis: A Translation with Commentaries

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions (Operator Theory: Advances and Applications, 304)

Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions (Progress in Mathematics, 289)

Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions (Progress in Mathematics, 289)

Slice Hyperholomorphic Schur Analysis (Operator Theory: Advances and Applications, 256)