A Modern Approach To Functional Integration

Author : John R. Klauder
Publisher : Springer Science & Business Media
ISBN 13 : 0817647910
Total Pages : 292 pages
Book Rating : 4.19/5 ( download)

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Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John R. Klauder
Publisher : Springer Science & Business Media
ISBN 13 : 0817647902
Total Pages : 292 pages
Book Rating : 4.02/5 ( download)

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Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Wolfgang Kollmann
Publisher : Springer Nature
ISBN 13 : 3030318699
Total Pages : 744 pages
Book Rating : 4.97/5 ( download)

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Download or read book Navier-Stokes Turbulence written by Wolfgang Kollmann and published by Springer Nature. This book was released on 2019-11-21 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean-Pierre Antoine
Publisher : Springer Science & Business Media
ISBN 13 : 1461570352
Total Pages : 354 pages
Book Rating : 4.56/5 ( download)

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Download or read book Functional Integration written by Jean-Pierre Antoine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Henri Bourles
Publisher : John Wiley & Sons
ISBN 13 : 1786309858
Total Pages : 324 pages
Book Rating : 4.53/5 ( download)

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Download or read book System Theory -- A Modern Approach, Volume 1 written by Henri Bourles and published by John Wiley & Sons. This book was released on 2024-07-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Martha Abell
Publisher : Springer Nature
ISBN 13 : 3030122778
Total Pages : 373 pages
Book Rating : 4.75/5 ( download)

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Download or read book Topics in Classical and Modern Analysis written by Martha Abell and published by Springer Nature. This book was released on 2019-10-21 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555502
Total Pages : 438 pages
Book Rating : 4.08/5 ( download)

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Download or read book Frames and Other Bases in Abstract and Function Spaces written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-06-11 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 510 pages
Book Rating : 4.60/5 ( download)

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Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hida Takeyuki
Publisher : World Scientific
ISBN 13 : 9813220953
Total Pages : 232 pages
Book Rating : 4.59/5 ( download)

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Download or read book Let Us Use White Noise written by Hida Takeyuki and published by World Scientific. This book was released on 2017-03-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel J. Greenhoe
Publisher : Abstract Space Publishing
ISBN 13 : 0983801134
Total Pages : 451 pages
Book Rating : 4.39/5 ( download)

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Download or read book Wavelet Structure and Design written by Daniel J. Greenhoe and published by Abstract Space Publishing. This book was released on 2013-08-21 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the structure of wavelets, principles of wavelet design, and mathematical structure that supports wavelet theory.