A Modern Approach To Functional Integration

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A Modern Approach to Functional Integration

John R. Klauder
A Modern Approach to Functional Integration Book PDF

Author : John R. Klauder
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,9 Mb
Release : 2010-11-08
Category : Mathematics
ISBN : 9780817647919

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A Modern Approach to Functional Integration by John R. Klauder Pdf

This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.

A Modern Approach to Functional Integration

John R. Klauder
A Modern Approach to Functional Integration Book PDF

Author : John R. Klauder
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 41,5 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9780817647902

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A Modern Approach to Functional Integration by John R. Klauder Pdf

This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.

Functional Integration

Jean-Pierre Antoine,Enrique Tirapegui
Functional Integration Book PDF

Author : Jean-Pierre Antoine,Enrique Tirapegui
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461570356

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Functional Integration by Jean-Pierre Antoine,Enrique Tirapegui Pdf

The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar ticles in which the main interest is the application to con crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.

Navier-Stokes Turbulence

Wolfgang Kollmann
Navier Stokes Turbulence Book PDF

Author : Wolfgang Kollmann
Publisher : Springer Nature
Page : 744 pages
File Size : 47,7 Mb
Release : 2019-11-21
Category : Science
ISBN : 9783030318697

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Navier-Stokes Turbulence by Wolfgang Kollmann Pdf

The book serves as a core text for graduate courses in advanced fluid mechanics and applied science. It consists of two parts. The first provides an introduction and general theory of fully developed turbulence, where treatment of turbulence is based on the linear functional equation derived by E. Hopf governing the characteristic functional that determines the statistical properties of a turbulent flow. In this section, Professor Kollmann explains how the theory is built on divergence free Schauder bases for the phase space of the turbulent flow and the space of argument vector fields for the characteristic functional. Subsequent chapters are devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their recognition.

System Theory -- A Modern Approach, Volume 1

Henri Bourles
System Theory A Modern Approach Volume 1 Book PDF

Author : Henri Bourles
Publisher : John Wiley & Sons
Page : 324 pages
File Size : 43,8 Mb
Release : 2024-07-11
Category : Mathematics
ISBN : 9781786309853

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System Theory -- A Modern Approach, Volume 1 by Henri Bourles Pdf

The theory of dynamic systems is addressed in this book in accordance with the “modern” approach, heir to algebraic analysis, which has been implemented since the last decade of the 20th century. After a reminder of the evolution of the representation of systems based on transfer functions or matrices, the duality of controllability and observability is revisited, and new results are produced concerning time-varying discrete-time systems. To complete and improve the existing analyses, the poles and zeros of linear systems and their interconnections are presented in a new way, as well as the problem of systems governed by functional differential equations (of retarded or neutral type) and their stabilization. This book also proposes known and original mathematical complements.

Topics in Classical and Modern Analysis

Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
Topics in Classical and Modern Analysis Book PDF

Author : Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
Publisher : Springer Nature
Page : 373 pages
File Size : 47,6 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783030122775

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Topics in Classical and Modern Analysis by Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu Pdf

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.

Frames and Other Bases in Abstract and Function Spaces

Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Frames and Other Bases in Abstract and Function Spaces Book PDF

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 438 pages
File Size : 47,7 Mb
Release : 2017-06-11
Category : Mathematics
ISBN : 9783319555508

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Frames and Other Bases in Abstract and Function Spaces by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Recent Applications of Harmonic Analysis to Function Spaces Differential Equations and Data Science Book PDF

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 510 pages
File Size : 45,9 Mb
Release : 2017-08-09
Category : Mathematics
ISBN : 9783319555560

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Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Let Us Use White Noise

Hida Takeyuki,Streit Ludwig
Let Us Use White Noise Book PDF

Author : Hida Takeyuki,Streit Ludwig
Publisher : World Scientific
Page : 232 pages
File Size : 45,6 Mb
Release : 2017-03-10
Category : Mathematics
ISBN : 9789813220959

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Let Us Use White Noise by Hida Takeyuki,Streit Ludwig Pdf

Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by "time". And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman "integral", wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's "integral" can now be understood, the "It's all in the vacuum" ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume. Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise. The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.

Wavelet Structure and Design

Daniel J. Greenhoe
Wavelet Structure and Design Book PDF

Author : Daniel J. Greenhoe
Publisher : Abstract Space Publishing
Page : 451 pages
File Size : 46,8 Mb
Release : 2013-08-21
Category : Mathematics
ISBN : 9780983801139

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Wavelet Structure and Design by Daniel J. Greenhoe Pdf

This book presents the structure of wavelets, principles of wavelet design, and mathematical structure that supports wavelet theory.

Coherent States and Their Applications

Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau
Coherent States and Their Applications Book PDF

Author : Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau
Publisher : Springer
Page : 347 pages
File Size : 52,5 Mb
Release : 2018-06-01
Category : Science
ISBN : 9783319767321

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Coherent States and Their Applications by Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau Pdf

Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.

Symmetries and Groups in Contemporary Physics

Chengming Bai
Symmetries and Groups in Contemporary Physics Book PDF

Author : Chengming Bai
Publisher : World Scientific
Page : 665 pages
File Size : 47,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814518550

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Symmetries and Groups in Contemporary Physics by Chengming Bai Pdf

This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange of ideas and methods in theoretical and mathematical physics.

Mathematical Feynman Path Integrals And Their Applications (Second Edition)

Sonia Mazzucchi
Mathematical Feynman Path Integrals And Their Applications Second Edition Book PDF

Author : Sonia Mazzucchi
Publisher : World Scientific
Page : 360 pages
File Size : 43,5 Mb
Release : 2021-11-16
Category : Science
ISBN : 9789811214806

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Mathematical Feynman Path Integrals And Their Applications (Second Edition) by Sonia Mazzucchi Pdf

Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.

Lectures on Constructive Approximation

Volker Michel
Lectures on Constructive Approximation Book PDF

Author : Volker Michel
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 55,8 Mb
Release : 2012-12-12
Category : Mathematics
ISBN : 9780817684037

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Lectures on Constructive Approximation by Volker Michel Pdf

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Functional Integration

Pierre Cartier,Cecile DeWitt-Morette
Functional Integration Book PDF

Author : Pierre Cartier,Cecile DeWitt-Morette
Publisher : Cambridge University Press
Page : 7 pages
File Size : 46,8 Mb
Release : 2006-11-30
Category : Science
ISBN : 9781139462884

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Functional Integration by Pierre Cartier,Cecile DeWitt-Morette Pdf

In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.