Spectral Theory On The S Spectrum For Quaternionic Operators

Author : Fabrizio Colombo,Jonathan Gantner,David P. Kimsey
Publisher : Springer
Page : 356 pages
File Size : 52,9 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.

Author : Fabrizio Colombo,Jonathan Gantner
Publisher : Springer
Page : 322 pages
File Size : 43,8 Mb
Release : 2019-07-10
Category : Mathematics
ISBN : 9783030164096

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Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes by Fabrizio Colombo,Jonathan Gantner Pdf

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
Page : 114 pages
File Size : 46,5 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442385

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Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators by Jonathan Gantner Pdf

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,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 126 pages
File Size : 48,5 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030502164

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Michele Sce's Works in Hypercomplex Analysis by Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

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 : Daniel Alpay,Fabrizio Colombo,Irene Sabadini
Publisher : Springer Nature
Page : 121 pages
File Size : 41,8 Mb
Release : 2020-01-27
Category : Mathematics
ISBN : 9783030383121

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Quaternionic de Branges Spaces and Characteristic Operator Function by Daniel Alpay,Fabrizio Colombo,Irene Sabadini Pdf

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 : Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 424 pages
File Size : 42,7 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9783031214608

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Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis by Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

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 : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen
Publisher : Birkhäuser
Page : 310 pages
File Size : 47,6 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 : M. Sh. Birman
Publisher : Springer Science & Business Media
Page : 96 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468475890

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Spectral Theory by M. Sh. Birman Pdf

Author : Jonathan Gantner
Publisher : American Mathematical Society
Page : 114 pages
File Size : 54,8 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442385

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Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators by Jonathan Gantner Pdf

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 : Aref Jeribi
Publisher : Springer
Page : 599 pages
File Size : 45,6 Mb
Release : 2015-07-04
Category : Science
ISBN : 9783319175669

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Spectral Theory and Applications of Linear Operators and Block Operator Matrices by Aref Jeribi Pdf

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 47,9 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author : César R. de Oliveira
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 50,8 Mb
Release : 2008-12-30
Category : Science
ISBN : 9783764387952

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Intermediate Spectral Theory and Quantum Dynamics by César R. de Oliveira Pdf

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. Many examples and exercises are included that focus on quantum mechanics.

Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa,Mihaela B. Vajiac
Publisher : Birkhäuser
Page : 398 pages
File Size : 49,9 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 : William Arveson
Publisher : Springer
Page : 142 pages
File Size : 42,8 Mb
Release : 2012-09-18
Category : Mathematics
ISBN : 1468492853

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A Short Course on Spectral Theory by William Arveson Pdf

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.

Author : Colette Moeglin,J. L. Waldspurger
Publisher : Cambridge University Press
Page : 382 pages
File Size : 53,8 Mb
Release : 1995-11-02
Category : Mathematics
ISBN : 0521418933

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Spectral Decomposition and Eisenstein Series by Colette Moeglin,J. L. Waldspurger Pdf

A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.