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This volume deals with the theory and applications of integraltransforms and convolutions of certain classes of integral,integrodifferential equations, and operational calculus. An extensivediscussion is presented, based on the universal hypergeometricapproach, i.e. many constructions of convolution and integraltransforms are obtained using the theory of Mellin--Barnes integralsand the Mellin transforms of hypergeometric type functions. Thisapproach is spread on so-called index transforms, in which theKontorovich--Lebedev and the Mehler--Fock transforms play a veryimportant part. The general constructions of index transforms aregiven and application to the evaluation of improper integral withrespect to a parameter of special function (index) is considered. Theoperational calculus for general integrodifferential operators isconstructed for both new types of convolutions. The book isself-contained, and includes a list of symbols with definitions,author and subject indices, and an up-to-date bibliography. This work will be of interest to researchers and graduate students inthe mathematical and physical sciences whose work involves integraltransforms and convolutions. ... Read more

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Thermal Quadrupoles describes a novel and powerful method which allows design engineers firstly to model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systematic methodological approach.

The chapters in this book increase in complexity from a rapid presentation of the method for one dimensional transient problems in Chapter one, to non-uniform boundary conditions or inhomogeneous media in Chapter six. In addition, a wide range of corrected problems of contemporary interest are presented mainly in Chapters three and six with their numerical implementation in MATLAB language. This book covers the whole scope of linear problems and presents a wide range of concrete issues of contemporary interest such as harmonic excitations of buildings, transfer in composite media, thermal contact resistance and moving material heat transfer. Extensions of this method to coupled transfers in a semi-transparent medium and to mass transfer in porous media are considered respectively in Chapters seven and eight. Chapter nine is devoted to practical numerical methods that can be used to inverse the Laplace transform.

Written from an engineering perspective, with applications to real engineering problems, this book will be of significant interest not only to researchers, lecturers and graduate students in mechanical engineering (thermodynamics) and process engineers needing to model a heat transfer problem to obtain optimized operating conditions, but also to researchers interested in the simulation or design of experiments where heat transfer plays a significant role. ... Read more

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This book is an approachable introduction to the theory of distributions and integral transforms.The principle intention of the book is to emphasize the remarkable connections of distribution theory with the classical analysis and the theory of differential equations. It covers the theory of the Lebesque integral as a fundamental tool in the proofs of many theorems.It gives practical hints on using the theory of distributions in cases where classical analysis is insufficient.The seven chapters of the book naturally connect general theory, examples and applications, and the authors attempt to answer natural questions related to topics presented in the text. It will be of interest to mathematicians, physicists, and researchers concerned with distribution theory and its applications to many fields of applied sciences. ... Read more

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The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind. ... Read more

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This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces. ... Read more

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Exploring integral transforms of generalized functions, this book covers such topics as the Laplace and Mellin transformations, the Weierstrass transformation, transformations involving hypergeometric functions and the G- and H- transformations. ... Read more

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This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results. ... Read more

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Integral Transforms in Computational Heat and Fluid Flow is a comprehensive volume that emphasizes the generalized integral transform technique (G.I.T.T.) and the developments that have made the technique a powerful computational tool of practical interest.The book progressively demonstrates the approach through increasingly difficult extensions and test problems.It begins with an overview of the generalized integral transform technique in contrast with classical analytical ideas.Various applications are presented throughout the book, including transient fin analysis with time-dependent surface dissipation, laminar forced convection inside externally finned tubes, metals oxidation at high temperatures, forced convection in liquid metals, and Navier-Stokes equations. ... Read more

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Very Good Book
If you work with the GITT (General Integral Transform Techinique), solving fluid mechanics and heat transfer problems on a pos-graduate level, so this is your Bible. A little confusing on the nomenclature for beginners, but itis not a big problem if you already have same experinece with theequations. ... Read more

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The book may be considered as a systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. The considered product kernels cover that case when factors of kernels have essential (less than one) singularities. The book intends to make a breakthrough in two directions: to cover multidimensional potentials, Hilbert transforms, strong maximal functions and at the same time, to present solutions of two-weighted problems for them which are much more complicated than one-weighted ones. In the given monograph two-weighted boundedness criteria for multiple Hardy transforms is reflected in the case when the two-dimensional weight on the right-hand side of an appropriate inequality is a product of two weight functions of single variable. In this case we present simpler and transparent criteria than those of E Sawyer for general weights. Moreover, we prove some new multidimensional Hardy type inequalities with general kernels. Weighted integral in-equalities for monotonic functions of several variables are also discussed.The main subjects of this book can be useful for applications both within various areas of the mathematical sciences (e.g. Fourier and Harmonic analysis, Fractional Calculus, BVP of PDE in Mathematical Physics, Stochastic Processes, Error Estimates in Numerical Analysis, etc.) as well as directly in some applied sciences. ... Read more

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Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

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H-Transforms: Theory and Applications presents a unified approach to the study of a wide class of integral transforms containing H- functions as kernels-or H-transforms-and their applications. It provides a general introduction to the theory of integral transforms and details the existence, representation, expansion, and properties of H-transforms. Discussions also include applications of integral transforms with kernels involving the Meijer G-transform and special functions of hypergeometric and Bessel type. This book will not only appeal to postgraduates and researchers in pure and applied mathematics, but also to also specialists in physics, mechanics, and engineering. ... Read more

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This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over  lines, planes, and spheres. Recent results are collected stressing explicit analytic methods. Another focus consists of the relations between algebraic integral geometry and partial differential equations.
A concise basic course in harmonic analysis and distribution theory is given in the first chapter. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data. It will be of particular interest to application oriented readers. Further chapters are devoted to the Funk-Radon transform on algebraic varieties of arbitrary dimension.
The material appeals to graduates and researchers in pure and applied mathematics who are interested in image reconstruction, inverse problems or functional analysis.

Customer Reviews (1)

For those who want to look more deeply into tomography
This book is an excellent bridge to the more advanced mathematical literature, and a good follow up to Natterer's review of the subject.The contributions of Gelfand and his school to this beautiful subject are deep and wide ranging, and well worth pursuing.

Problems with typos in this edition, and skimpy detail on some of the proofs do subtract somewhat from the overall rating, however.I hope the author will produce a second edition. ... Read more

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This book provides a modern treatment of the theory of complex variables and transform calculus and their applications to physical problems. Although intended primarily for undergraduate students, certain parts of the text may be useful for graduate students and mathematical technologists working in industry. It is intended for a one-semester course at undergraduate mathematics level basically for science and engineering students. It can also be used by the graduate students of applied science.

The text includes complex numbers, analytic function of a complex variable, integration in a complex domain, Taylor and Laurent series expansions, theory of residue calculus, Fourier Transforms, Laplace transforms, conformal mapping, applications to physical problems and analytic continuation of a function into a domain in the complex plane.

Matiur Rahman is a leading figure in engineering mathematics, with over 25 years of lecturing experience at the Technical University of Nova Scotia. ... Read more

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The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. It focuses on integral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes, etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. We provide a list of problems which were open at the time of completion of the book.
Audience: The book is aimed at a rather wide audience, ranging from researchers in functional and harmonic analysis to experts in applied mathematics and prospective students. ... Read more