Study Of Compact Quantum Groups With Probabilistic Methods
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Study Of Compact Quantum Groups With Probabilistic Methods
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Author : Souleiman Omar hoch
language : en
Publisher:
Release Date : 2017
Study Of Compact Quantum Groups With Probabilistic Methods written by Souleiman Omar hoch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
This thesis studies problems linked to the lattice of quantum subgroups and characterizationof ergodic actions and idempotent states of a compact quantum group. It consistsof three parts. The first part present some preliminary results about locally compactquantum groups, normal quantum subgroups, ergodic actions and idempotent states. Thesecond part studies the quantum analog of Dedekind's modularity law, Noether's isomorphismtheorem and their consequences as the Schreier refinement theorem and theJordan-Hölder theorem. This part completes the work of Shuzhou WANG on the quantumanalog of the third isomorphism theorem for compact quantum group and the recentwork of Kasprzak, Khosravi and Soltan on the quantum analog of the first Noether isomorphismtheorem for locally compact quantum groups. In the third part, we characterizeidempotent states of the compact quantum group O-1(2) relying on the characterizationof embeddable ergodic actions. This third part is in the sequence of the seminal works ofFranz, Skalski and Tomatsu for the compact quantum groups Uq(2), SUq(2) and SOq(3).We classify in advance the ergodic actions and embeddable ergodic actions of the compactquantum group O-1(2).This thesis is based on two papers of the author and al. The first one is entitled"Fundamental isomorphism theorems for quantum groups" which have been accepted forpublication in Expositionae Mathematicae and the second one is entitled "Ergodic actionsand idempotent states of O-1(2)" and is being finalized for submission.
Fundamentals Of Classical Fourier Analysis
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Author : Shashank Tiwari
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Fundamentals Of Classical Fourier Analysis written by Shashank Tiwari and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Fundamentals of Classical Fourier Analysis" is a comprehensive guide to understanding fundamental concepts, techniques, and applications of Fourier analysis in classical mathematics. This book provides a thorough exploration of Fourier analysis, from its historical origins to modern-day applications, offering readers a solid foundation in this essential area of mathematics. Classical Fourier analysis has been a cornerstone of mathematics and engineering for centuries, playing a vital role in solving problems in fields like signal processing, differential equations, and quantum mechanics. We delve into the rich history of Fourier analysis, tracing its development from Joseph Fourier's groundbreaking work to modern digital signal processing applications. Starting with an overview of fundamental concepts and motivations behind Fourier analysis, we introduce Fourier series and transforms, exploring their properties, convergence, and applications. We discuss periodic and non-periodic functions, convergence phenomena, and important theorems such as Parseval's identity and the Fourier inversion theorem. Throughout the book, we emphasize both theoretical insights and practical applications, providing a balanced understanding of Fourier analysis and its relevance to real-world problems. Topics include harmonic analysis, orthogonal functions, Fourier integrals, and Fourier transforms, with applications in signal processing, data compression, and partial differential equations. Each chapter includes examples, illustrations, and exercises to reinforce key concepts. Historical insights into key mathematicians and scientists' contributions are also provided. Whether you are a student, researcher, or practitioner in mathematics, engineering, or related fields, "Fundamentals of Classical Fourier Analysis" is a comprehensive and accessible resource for mastering Fourier analysis principles and techniques.
Algebraic Methods In Functional Analysis
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Author : Ivan G. Todorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-25
Algebraic Methods In Functional Analysis written by Ivan G. Todorov 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 2013-10-25 with Mathematics categories.
This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his 65th birthday. The papers included in the volume cover a large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups, and reflect recent developments in these areas. The book consists of both original research papers and high quality survey articles, all of which were carefully refereed.
Analysis And Quantum Groups
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Author : Lars Tuset
language : en
Publisher: Springer Nature
Release Date : 2022-07-27
Analysis And Quantum Groups written by Lars Tuset and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-27 with Mathematics categories.
This volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of ‘Haar integrals’ on locally compact quantum groups, and is thus treated quite extensively The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.
Characterization Of Probability Distributions On Locally Compact Abelian Groups
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Author : Gennadiy Feldman
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
Characterization Of Probability Distributions On Locally Compact Abelian Groups written by Gennadiy Feldman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.
Quantum Isometry Groups
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Author : Debashish Goswami
language : en
Publisher: Springer
Release Date : 2017-01-05
Quantum Isometry Groups written by Debashish Goswami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-05 with Mathematics categories.
This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
Introduction To Quantum Groups
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Author : Teo Banica
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Introduction To Quantum Groups written by Teo Banica and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter–Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
Topological Phases Of Matter And Quantum Computation
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Author : Paul Bruillard
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-31
Topological Phases Of Matter And Quantum Computation written by Paul Bruillard 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 2020-03-31 with Education categories.
This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24–25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments. The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Applications Of Hypergroups And Related Measure Algebras
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-02-28
Applications Of Hypergroups And Related Measure Algebras written by 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 1995-02-28 with Mathematics categories.
`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.