Hypercomplex Analysis New Perspectives And Applications

Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen
Publisher : Springer
Page : 227 pages
File Size : 52,7 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319087719

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Hypercomplex Analysis: New Perspectives and Applications by Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen Pdf

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.

Author : Irene Sabadini,Michael Shapiro,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 45,5 Mb
Release : 2009-04-21
Category : Mathematics
ISBN : 9783764398934

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Hypercomplex Analysis by Irene Sabadini,Michael Shapiro,Franciscus Sommen Pdf

Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.

Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen
Publisher : Birkhäuser
Page : 310 pages
File Size : 40,7 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783319425290

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Modern Trends in Hypercomplex Analysis by Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen Pdf

This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.

Author : Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
Publisher : Springer Nature
Page : 389 pages
File Size : 55,6 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030764739

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New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative by Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac Pdf

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.

Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer
Page : 118 pages
File Size : 48,8 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9783319492650

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Entire Slice Regular Functions by Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

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.

Author : Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot
Publisher : Birkhäuser
Page : 283 pages
File Size : 42,7 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319291161

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Noncommutative Analysis, Operator Theory and Applications by Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot Pdf

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Author : Beniamino Murgante,Sanjay Misra,Ana Maria Alves Coutinho Rocha,Carmelo Torre,Jorge Gustavo Rocha,Maria Irene Falcão,David Taniar,Bernady O. Apduhan,Osvaldo Gervasi
Publisher : Springer
Page : 838 pages
File Size : 55,9 Mb
Release : 2014-07-03
Category : Computers
ISBN : 9783319091440

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Computational Science and Its Applications - ICCSA 2014 by Beniamino Murgante,Sanjay Misra,Ana Maria Alves Coutinho Rocha,Carmelo Torre,Jorge Gustavo Rocha,Maria Irene Falcão,David Taniar,Bernady O. Apduhan,Osvaldo Gervasi Pdf

The six-volume set LNCS 8579-8584 constitutes the refereed proceedings of the 14th International Conference on Computational Science and Its Applications, ICCSA 2014, held in Guimarães, Portugal, in June/July 2014. The 347 revised papers presented in 30 workshops and a special track were carefully reviewed and selected from 1167 initial submissions. The 289 papers presented in the workshops cover various areas in computational science ranging from computational science technologies to specific areas of computational science such as computational geometry and security.

Author : Paula Cerejeiras,Craig A. Nolder,John Ryan,Carmen Judith Vanegas Espinoza
Publisher : Springer
Page : 152 pages
File Size : 52,5 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783030000493

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Clifford Analysis and Related Topics by Paula Cerejeiras,Craig A. Nolder,John Ryan,Carmen Judith Vanegas Espinoza Pdf

This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods and theorems from complex analysis generalize to higher dimensions in various ways. However, many new features emerge in the process, and much of this work is still in its infancy. Some of the leading mathematicians working in this field have contributed to this book in conjunction with “Clifford Analysis and Related Topics: a conference in honor of Paul A.M. Dirac,” which was held at Florida State University, Tallahassee, on December 15-17, 2014. The content reflects talks given at the conference, as well as contributions from mathematicians who were invited but were unable to attend. Hence much of the mathematics presented here is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the book will be of interest to mathematicians and physicists working in these areas, as well as students seeking to catch up on the latest developments.

Author : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Publisher : Springer
Page : 390 pages
File Size : 45,8 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783034809641

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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Pdf

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.

Author : Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau
Publisher : Springer
Page : 347 pages
File Size : 50,6 Mb
Release : 2018-06-01
Category : Science
ISBN : 9783319767321

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Coherent States and Their Applications by Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau Pdf

Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.

Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa,Mihaela B. Vajiac
Publisher : Birkhäuser
Page : 398 pages
File Size : 42,5 Mb
Release : 2017-09-30
Category : Mathematics
ISBN : 9783319623627

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Advances in Complex Analysis and Operator Theory by Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa,Mihaela B. Vajiac Pdf

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 : Graziano Gentili,Caterina Stoppato,Daniele C. Struppa
Publisher : Springer Nature
Page : 302 pages
File Size : 46,9 Mb
Release : 2022-09-23
Category : Mathematics
ISBN : 9783031075315

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Regular Functions of a Quaternionic Variable by Graziano Gentili,Caterina Stoppato,Daniele C. Struppa Pdf

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 : Michael Ruzhansky
Publisher : Springer Nature
Page : 239 pages
File Size : 45,8 Mb
Release : 2024-06-12
Category : Electronic
ISBN : 9783031416651

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Extended Abstracts MWCAPDE 2023 by Michael Ruzhansky Pdf

Author : Daniel Alpay,Fabrizio Colombo,Irene Sabadini
Publisher : Birkhäuser
Page : 362 pages
File Size : 44,7 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9783319425146

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Slice Hyperholomorphic Schur Analysis by Daniel Alpay,Fabrizio Colombo,Irene Sabadini Pdf

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.

Author : Fabrizio Colombo,Jonathan Gantner,David P. Kimsey
Publisher : Springer
Page : 356 pages
File Size : 46,9 Mb
Release : 2019-01-04
Category : Mathematics
ISBN : 9783030030742

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Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo,Jonathan Gantner,David P. Kimsey Pdf

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.