The Weyl Operator And Its Generalization
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The Weyl Operator And Its Generalization
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Author : Leon Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13
The Weyl Operator And Its Generalization written by Leon Cohen 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 2012-12-13 with Mathematics categories.
The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes
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Author : Maurice A De Gosson
language : en
Publisher: World Scientific
Release Date : 2017-11-10
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes written by Maurice A De Gosson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Science categories.
The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.
Quantum Harmonic Analysis
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Author : Maurice A. de Gosson
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-07-05
Quantum Harmonic Analysis written by Maurice A. de Gosson and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Mathematics categories.
Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Analysis Of Pseudo Differential Operators
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Author : Shahla Molahajloo
language : en
Publisher: Springer
Release Date : 2019-05-08
Analysis Of Pseudo Differential Operators written by Shahla Molahajloo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-08 with Mathematics categories.
This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.
Advances In Microlocal And Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-03-03
Advances In Microlocal And Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-03 with Mathematics categories.
The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Commutation Relations Normal Ordering And Stirling Numbers
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Author : Toufik Mansour
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Commutation Relations Normal Ordering And Stirling Numbers written by Toufik Mansour and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow
Landscapes Of Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Landscapes Of Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory Modulation space theory Applications to the medical industry Wavelet transform theory Anti-Wick operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Excursions In Harmonic Analysis Volume 6
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Author : Matthew Hirn
language : en
Publisher: Springer Nature
Release Date : 2021-09-01
Excursions In Harmonic Analysis Volume 6 written by Matthew Hirn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Mathematics categories.
John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Fredholm And Local Spectral Theory Ii
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Author : Pietro Aiena
language : en
Publisher: Springer
Release Date : 2018-11-24
Fredholm And Local Spectral Theory Ii written by Pietro Aiena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.
This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.
Scientia Magna Vol 7 No 1 2011
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Author : Zhang Wenpeng
language : en
Publisher: Infinite Study
Release Date :
Scientia Magna Vol 7 No 1 2011 written by Zhang Wenpeng and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Papers on Smarandache isotopy of second Smarandache Bol loops, dual quaternions and matrices of dual quaternions, generalized Weyl's theorem for Class A operators, a result about Young's inequality and several applications, minimal translation lightlike hypersurfaces, inequalities between the sides and angles of an acute triangle, and similar topics. Contributors: M. A. Gungor, M. Sarduvan, J. Tian, W. He, G. Ilango, R. Marudhachalam, R. Poovazhaki, V. Swaminathan, M. Mohamadhasani, M. Haveshki, A. N. Murugan, A. Nagarajan, S. Harmaitree, U. Leerawat, and others.