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Quantum Harmonic Analysis

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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.

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

Symplectic Methods In Harmonic Analysis And In Mathematical Physics

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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-30

Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by Maurice A. de Gosson 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 2011-07-30 with Mathematics categories.

The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.

Harmonic Analysis On The Heisenberg Group

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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-24

Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu 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 1998-03-24 with Mathematics categories.

This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and, hence gives the greatest opportunity for generalizing the remarkable results of Euclidian harmonic analysis.

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.

Introduction To Classical And Quantum Harmonic Oscillators

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Author : S. C. Bloch
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-29

Introduction To Classical And Quantum Harmonic Oscillators written by S. C. Bloch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-29 with Science categories.

From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating concepts, key to understanding the physical universe and a linchpin in fields as diverse as mechanics, electromagnetics, electronics, optics, acoustics, and quantum mechanics. Complete with disk, Introduction to Classical and Quantum Harmonic Oscillators is a hands-on guide to understanding how harmonic oscillators function and the analytical systems used to describe them. Professionals and students in electrical engineering, mechanical engineering, physics, and chemistry will gain insight in applying these analytical techniques to even more complex systems. With the help of spreadsheets ready to run on Microsoft Excel (or easily imported to Quattro Pro or Lotus 1-2-3), users will be able to thoroughly and easily examine concepts and questions, of considerable difficulty and breadth, without painstaking calculation. The software allows users to imagine, speculate, and ask "what if .?" and then instantly see the answer. You're not only able to instantly visualize results but also to interface with data acquisition boards to import real-world information. The graphic capability of the software allows you to view your work in color and watch new results blossom as you change parameters and initial conditions. Introduction to Classical and Quantum Harmonic Oscillators is a practical, graphically enhanced excursion into the world of harmonic oscillators that lets the reader experience and understand their utility and unique contribution to scientific understanding. It also describes one of the enduring themes in scientific inquiry, begun in antiquity and with an as yet unimagined future.

Functional Analysis

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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Functional Analysis written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This book, Functional Analysis, is designed for absolute beginners who want to understand the fundamental ideas of functional analysis without advanced prerequisites. Starting from the basics, it introduces concepts like vector spaces, norms, and linear operators, using simple explanations and examples to build a strong foundation. Each chapter breaks down complex topics step-by-step, making it accessible for anyone new to the subject. By the end, readers will have a clear understanding of the core principles of functional analysis and how these ideas apply in mathematics, physics, and engineering.

The Scope And History Of Commutative And Noncommutative Harmonic Analysis

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Author : George W. Mackey
language : en
Publisher: American Mathematical Soc.
Release Date : 2005-04-08

The Scope And History Of Commutative And Noncommutative Harmonic Analysis written by George W. Mackey 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 2005-04-08 with Mathematics categories.

''When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric ... The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations--discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated. Information for our distributors: Copublished with the London Mathematical Society beginning with volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Harmonic Analysis On Symmetric Spaces Higher Rank Spaces Positive Definite Matrix Space And Generalizations

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Author : Audrey Terras
language : en
Publisher: Springer
Release Date : 2016-04-26

Harmonic Analysis On Symmetric Spaces Higher Rank Spaces Positive Definite Matrix Space And Generalizations written by Audrey Terras and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Mathematics categories.

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Fuzzy Analysis

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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-24

Fuzzy Analysis written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-24 with Mathematics categories.

Introduces fuzzy set theory and logic, with applications in decision-making, control systems, and data analysis in uncertain environments.

Quantum Harmonic Analysis

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