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The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in quantum theory, the mathematically beautiful but difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the four approaches to the Feynman integral which are given detailed treatment in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed and detailed proofs are provided for the central results. ... Read more

Customer Reviews (1)

An Excellent Volume!
This volume by Johnson and Lapidus is an excellent guide to the Feynman integral and Feynman's operational calculus. The authors bring together a great deal of the background material needed for the study of the integral and operational calculus so as to make the volume mostly self-contained.

The book contains several different approaches to the Feynman integral and discusses in some detail relationships between these approaches. The exposition is very clear and detailed and the proofs of results in the text are detailed and extremely well written. Also, the text contains many items that have only appeared in the research literature. Some of these results are quite new.

Also contained in this text is a thorough discussion of Feynman's operational calculus, again from more than one point of view. Many of the results contained here have only appeared previously in the research literature and again some are quite recent. This part of the book is also very well and clearly written.

There are also many remarks and examples dealing with the applicability of the formalism to physical situations.

This is a great read for anyone wanting to further there knowledge about these subjects. ... Read more

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Electromagnetic Wave Propagation in Turbulence is devoted to a method for obtaining analytical solutions to problems of electromagnetic wave propagation in turbulence. In a systematic way the monograph presents the Mellin transforms to evaluate analytically integrals that are not in integral tables. Ample examples of application are outlined and solutions for many problems in turbulence theory are given. The method itself relates to asymptotic results that are applicable to a broad class of problems for which many asymptotic methods had to be employed previously. ... Read more

Customer Reviews (1)

Great treatise for learning + invaluable reference
If you're into atmospheric turbulence statistics, propagation in turbulence or just Mellin transforms, this book is a treasure. In a veritable tour de force, Sasiela starts from the Rytov approximation and derives analytical results for a variety of phenomena, including adaptive optics, anisoplantism, scintillation and many more. It has been my primary source for theoretical analysis in this topic since I got the book, and I haven't seen a better one yet. ... Read more

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Chapters: Fourier Analysis, Wavelet Transform, Fourier Transform, List of Fourier-Related Transforms, Laplace Transform, Hilbert Transform, Mellin Transform, Weierstrass Transform, Radon Transform, Mellin Inversion Theorem, Integral Transform, Fractional Fourier Transform, Linear Canonical Transformation, Riemann-liouville Integral, Sumudu Transform, Continuous Wavelet Transform, Motions in the Time-Frequency Distribution, Laplace-stieltjes Transform, Hartley Transform, Abel Transform, Riesz Transform, Hankel Transform, Nachbin's Theorem, Projection-Slice Theorem, Constant Q Transform, Funk Transform, Gabor Transform, Triple Correlation, Nörlund-rice Integral, Two-Sided Laplace Transform, Sine and Cosine Transforms, Inverse Laplace Transform, Stieltjes Transformation, Bicoherence, Bispectrum, Gabor-Wigner Transform, Laplace Transform Applied to Differential Equations, Perron's Formula, Fourier Operator, X-Ray Transform, Post's Inversion Formula, Kontorovich-Lebedev Transform. Source: Wikipedia. Pages: 221. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, the Fourier transform (often abbreviated FT) is an operation that transforms one complex-valued function of a real variable into another. In such applications as signal processing, the domain of the original function is typically time and is accordingly called the time domain. That of the new function is frequency, and so the Fourier transform is often called the frequency domain representation of the original function. It describes which frequencies are present in the original function. This is analogous to describing a chord of music in terms of the notes being played. In effect, the Fourier transform decomposes a function into oscillatory functions. The term Fourier transform refers both to the frequency domain representat...More: http://booksllc.net/?id=52247 ... Read more

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A comprehensive exposition on analytic methods for solving science and engineering problems, this text is written from the viewpoint of distribution theory and includes a number of current topics relevant to practitioners and researchers. ... Read more

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Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The goal of the book is to give the reader, specialist and non-specialist useable and modern mathematical tools in their research and analysis.

This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

Features:

Application-oriented exposition of distributional calculus including solutions of ordinary differential equations. Abstract formalism is kept to a minimum.

Detailed coverage of asymptotic methods, including the stationary phase and steepest descent methods, for Fourier and other integral transforms from an applications perspective

Modern topics such as fractional calculus, uncertainty principle, wavelets, and multi-resolution analysis

Extensive use of real word applications from fluid mechanics, wave propagation, optics, relaxation phenomena, etc., in examples and extensive exercise sets. Solution and/or answers to exercises are carefully worked out at the end of the book.

Clear explanations, motivation, and illustration of all necessary mathematical concepts. ... Read more

Customer Reviews (1)

Excellent Introduction
This book provides a simple, example-based discussion of its subtle subject matter which will have you conversant in the material in no time. It gets to the ideas of the subject without making you wade through pagesof formalism and abstraction first. This is science writing at its best. ... Read more

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This digital document is a journal article from Environmental Modelling and Software, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The Generalized Integral Transform Technique (GITT) is employed to obtain numerical-analytical solutions for mathematical models that predict the dispersion of dissolved pollutants in rivers, streams and channels with either symmetric or asymmetric flow. The two-dimensional steady-state model presented allows for the use of variable coefficients represented by non-uniform velocity profiles and turbulent diffusion coefficients, in any general functional form. The proposed model is then applied to an example of biocides contamination downstream of thermohydroelectric power stations, originated from the cleaning of cooling water systems undergoing biofouling. ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Integral Transforms, Fourier Analysis, Wavelet Transform, Fourier Transform, List of Fourier-Related Transforms, Laplace Transform, Hilbert Transform, Mellin Transform, Weierstrass Transform, Radon Transform, Mellin Inversion Theorem, Fractional Fourier Transform, Linear Canonical Transformation, Stochastic Geometry, Riemann-liouville Integral, Sumudu Transform, Continuous Wavelet Transform, Motions in the Time-Frequency Distribution, Laplace-stieltjes Transform, Buffon's Needle, Hartley Transform, Abel Transform, Riesz Transform, Hankel Transform, Nachbin's Theorem, Projection-Slice Theorem, Constant Q Transform, Funk Transform, Gabor Transform, Prékopa-leindler Inequality, Triple Correlation, Nörlund-rice Integral, Two-Sided Laplace Transform, Sine and Cosine Transforms, Borell-brascamp-lieb Inequality, Buffon's Noodle, Crofton Formula, Inverse Laplace Transform, Stieltjes Transformation, Bicoherence, Bispectrum, Penrose Transform, Gabor-Wigner Transform, Laplace Transform Applied to Differential Equations, Perron's Formula, Fourier Operator, X-Ray Transform, Post's Inversion Formula, Hadwiger's Theorem, Kontorovich-Lebedev Transform, Bateman Transform, Pompeiu Problem. Excerpt:In the mathematical study of partial differential equation , the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables . It is named after the English mathematician Harry Bateman , who first published the result in (Bateman 1904).The formula asserts that if is a holomorphic function of three complex variables, thenis a solution of the Laplace equation, which follows by differentiation under the integral. Furthermore, Bateman asserted that the most general solution of t... ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Singular Integrals, Fourier Analysis, Wavelet Transform, Fourier Transform, List of Fourier-Related Transforms, Laplace Transform, Hilbert Transform, Mellin Transform, Weierstrass Transform, Radon Transform, Mellin Inversion Theorem, Integral Transform, Fractional Fourier Transform, Linear Canonical Transformation, Riemann-liouville Integral, Sumudu Transform, Continuous Wavelet Transform, Motions in the Time-Frequency Distribution, Laplace-stieltjes Transform, Hartley Transform, Abel Transform, Riesz Transform, Hankel Transform, Newtonian Potential, Nachbin's Theorem, Projection-Slice Theorem, Constant Q Transform, Funk Transform, Gabor Transform, Triple Correlation, Nörlund-rice Integral, Two-Sided Laplace Transform, Riesz Potential, Sine and Cosine Transforms, Inverse Laplace Transform, Stieltjes Transformation, Bicoherence, Bispectrum, Gabor-Wigner Transform, Laplace Transform Applied to Differential Equations, Perron's Formula, Fourier Operator, X-Ray Transform, Post's Inversion Formula, Kontorovich-Lebedev Transform, Bessel Potential. Excerpt:In mathematics , the Abel transform , named for Niels Henrik Abel , is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f (r ) is given by:Assuming f (r ) drops to zero more quickly than 1/r , the inverse Abel transform is given byIn image analysis , the forward Abel transform is used to project an optically thin, axially symmetric emission function onto a plane, and the reverse Abel transform is used to calculate the emission function given a projection (i.e. a scan or a photograph) of that emission function.In recent years, the inverse Abel transformation (and its variants) has become the cornerstone of data analysis in photofragment-ion im... ... Read more

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This is the first of three major volumes which present acomprehensive treatment of the theory of the main classes of specialfunctions from the point of view of the theory of grouprepresentations.
This volume deals with the properties of classical orthogonalpolynomials and special functions which are related to representationsof groups of matrices of second order and of groups of triangularmatrices of third order. This material forms the basis of many resultsconcerning classical special functions such as Bessel, MacDonald,Hankel, Whittaker, hypergeometric, and confluent hypergeometricfunctions, and different classes of orthogonal polynomials, includingthose having a discrete variable. Many new results are given.
The volume is self-contained, since an introductory section presentsbasic required material from algebra, topology, functional analysisand group theory.
For research mathematicians, physicists and engineers. ... Read more