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Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory


Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory
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Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory


Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory
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Author : Roland Speicher
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory written by Roland Speicher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.


Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.



Advances In Complex Analysis And Operator Theory


Advances In Complex Analysis And Operator Theory
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Author : Fabrizio Colombo
language : en
Publisher: Birkhäuser
Release Date : 2017-09-30

Advances In Complex Analysis And Operator Theory written by Fabrizio Colombo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-30 with Mathematics categories.


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.



Number Theory And Symmetry


Number Theory And Symmetry
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Author : Michel Planat
language : en
Publisher: MDPI
Release Date : 2021-01-20

Number Theory And Symmetry written by Michel Planat and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Computers categories.


According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.



Spectral Properties Of Certain Operators On A Free Hilbert Space And The Semicircular Law


Spectral Properties Of Certain Operators On A Free Hilbert Space And The Semicircular Law
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Author : Ilwoo Cho
language : en
Publisher: Elsevier
Release Date : 2023-04-21

Spectral Properties Of Certain Operators On A Free Hilbert Space And The Semicircular Law written by Ilwoo Cho and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-21 with Mathematics categories.


In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how "free-Hilbert-space Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how "inside actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law. - Presents the spectral properties of three types of operators on a Hilbert space, in particular how these operators affect the semicircular law - Demonstrates how the semicircular law is deformed by actions "from inside", as opposed to actions "from outside" considered by previous theory - Explores free Hilbert spaces and their modeling applications - Authored by two leading researchers in Operator Theory and Operator Algebra



Quantum Probability And Infinite Dimensional Analysis Proceedings Of The Conference


Quantum Probability And Infinite Dimensional Analysis Proceedings Of The Conference
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Author : Wolfgang Freudenberg
language : en
Publisher: World Scientific
Release Date : 2003-01-28

Quantum Probability And Infinite Dimensional Analysis Proceedings Of The Conference written by Wolfgang Freudenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-28 with Mathematics categories.


This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, quantum Markov processes, the stochastic limit, quantum teleportation and other areas.



Proceedings Of The Conference Quantum Probability And Infinite Dimensional Analysis


Proceedings Of The Conference Quantum Probability And Infinite Dimensional Analysis
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Author : Wolfgang Freudenberg
language : en
Publisher: World Scientific
Release Date : 2003

Proceedings Of The Conference Quantum Probability And Infinite Dimensional Analysis written by Wolfgang Freudenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.


This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, the stochastic limit, quantum teleportation and other areas. Contents: Markov Property -- Recent Developments on the Quantum Markov Property (L Accardi & F Fidaleo); Stationary Quantum Stochastic Processes from the Cohomological Point of View (G G Amosov); The Feller Property of a Class of Quantum Markov Semigroups II (R Carbone & F Fagnola); Recognition and Teleportation (K-H Fichtner et al.); Prediction Errors and Completely Positive Maps (R Gohm); Multiplicative Properties of Double Stochastic Product Integrals (R L Hudson); Isometric Cocycles Related to Beam Splittings (V Liebscher); Multiplicativity via a Hat Trick (J M Lindsay & S J Wills); Dilation Theory and Continuous Tensor Product Systems of Hilbert Modules (M Skeide); Quasi-Free Fermion Planar Quantum Stochastic Integrals (W J Spring & I F Wilde); and other papers.



Encyclopedia Of Nonlinear Science


Encyclopedia Of Nonlinear Science
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Author : Alwyn Scott
language : en
Publisher: Routledge
Release Date : 2006-05-17

Encyclopedia Of Nonlinear Science written by Alwyn Scott and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-17 with Reference categories.


In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.



New Trends In Applied Analysis And Computational Mathematics


New Trends In Applied Analysis And Computational Mathematics
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Author : Susanta Kumar Paikray
language : en
Publisher: Springer Nature
Release Date : 2021-06-28

New Trends In Applied Analysis And Computational Mathematics written by Susanta Kumar Paikray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Technology & Engineering categories.


The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.



Mathematical Physics Ii


Mathematical Physics Ii
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Author : Enrico De Micheli
language : en
Publisher: MDPI
Release Date : 2020-12-15

Mathematical Physics Ii written by Enrico De Micheli and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.


The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.



Quantum Probability And Spectral Analysis Of Graphs


Quantum Probability And Spectral Analysis Of Graphs
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Author : Akihito Hora
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05

Quantum Probability And Spectral Analysis Of Graphs written by Akihito Hora and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Science categories.


This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.