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Noncommutative Functional Calculus
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Author :Prof. Fabrizio Colombo Politecnico di Milano Publisher :Springer Science & Business Media ISBN 13 :3034801106 Total Pages :228 pages Book Rating :4.0/5 (348 download)
Book Synopsis Noncommutative Functional Calculus by : Prof. Fabrizio Colombo Politecnico di Milano
Download or read book Noncommutative Functional Calculus written by Prof. Fabrizio Colombo Politecnico di Milano and published by Springer Science & Business Media. This book was released on 2011-03-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Functional Calculus by : Fabrizio Colombo
Download or read book Noncommutative Functional Calculus written by Fabrizio Colombo and published by . This book was released on 2011-03-30 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Noncommutative Functional Calculus by :
Download or read book Noncommutative Functional Calculus written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers by : Cédric Arhancet
Download or read book Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers written by Cédric Arhancet and published by Springer Nature. This book was released on 2022-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
Book Synopsis H^\infty Functional Calculus and Square Functions on Noncommutative L^p -spaces by : Marius Junge
Download or read book H^\infty Functional Calculus and Square Functions on Noncommutative L^p -spaces written by Marius Junge and published by . This book was released on 2006 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces by : Marius Junge
Download or read book H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces written by Marius Junge and published by . This book was released on 2006 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate sectorial operators and semigroups acting on noncommutative Lp-spaces. We introduce new square functions in this context and study their connection with H[infinity] functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative Lp-spaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative Lp-spaces. We mainly focus on noncommutative diffusion semigroups. We discuss several examples of such semigroups for which we establish bounded H[infinity] functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck semigroups acting on the q-deformed von Neumann algebras of Bozejko-Speicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Book Synopsis H[infinito] Functional Calculus and Square Functions on Noncommutative Lp-spaces by : Marius Junge
Download or read book H[infinito] Functional Calculus and Square Functions on Noncommutative Lp-spaces written by Marius Junge and published by . This book was released on 2006 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Calculus written by Kamal Shah and published by BoD – Books on Demand. This book was released on 2020-06-17 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.
Book Synopsis Non-commutative Analysis by : Palle Jorgensen
Download or read book Non-commutative Analysis written by Palle Jorgensen and published by World Scientific. This book was released on 2017-01-24 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Author :Dmitry S. Kaliuzhnyi-Verbovetskyi Publisher :American Mathematical Soc. ISBN 13 :1470416972 Total Pages :194 pages Book Rating :4.4/5 (74 download)
Book Synopsis Foundations of Free Noncommutative Function Theory by : Dmitry S. Kaliuzhnyi-Verbovetskyi
Download or read book Foundations of Free Noncommutative Function Theory written by Dmitry S. Kaliuzhnyi-Verbovetskyi and published by American Mathematical Soc.. This book was released on 2014-11-19 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.
Book Synopsis Functional Calculi by : Charles W Swartz
Download or read book Functional Calculi written by Charles W Swartz and published by World Scientific. This book was released on 2013-03-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining “functions of an operator”. Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.
Book Synopsis On Non-holomorphic Functional Calculus for Commuting Operators by : Sebastian Sandberg
Download or read book On Non-holomorphic Functional Calculus for Commuting Operators written by Sebastian Sandberg and published by . This book was released on 1999 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Noncommutative Function-Theoretic Operator Theory and Applications by : Joseph A. Ball
Download or read book Noncommutative Function-Theoretic Operator Theory and Applications written by Joseph A. Ball and published by Cambridge University Press. This book was released on 2021-12-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Book Synopsis H [symbole infini] functional calculus and square functions on noncommutative Lp-spaces by : Marius Junge
Download or read book H [symbole infini] functional calculus and square functions on noncommutative Lp-spaces written by Marius Junge and published by . This book was released on 2006 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Completing the Riesz-Dunford Functional Calculus by : John B. Conway
Download or read book Completing the Riesz-Dunford Functional Calculus written by John B. Conway and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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