Download or read book Plane Waves and Spherical Means written by F. John and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form. New Rochelle FRITZ JOHN September, 1955 [v] CONTENTS Introduction. . . . . . . 1 CHAPTER I Decomposition of an Arbitrary Function into Plane Waves Explanation of notation . . . . . . . . . . . . . . . 7 The spherical mean of a function of a single coordinate. 7 9 Representation of a function by its plane integrals . CHAPTER II Tbe Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients Hyperbolic equations. . . . . . . . . . . . . . . . . . . . . . 15 Geometry of the normal surface for a strictly hyperbolic equation. 16 Solution of the Cauchy problem for a strictly hyperbolic equation . 20 Expression of the kernel by an integral over the normal surface. 23 The domain of dependence . . . . . . . . . . . . . . . . . . . 29 The wave equation . . . . . . . . . . . . . . . . . . . . . . 32 The initial value problem for hyperbolic equations with a normal surface having multiple points . . . . . . . . . . . . . . . . . . . . 36 CHAPTER III The Fundamental Solution of a Linear Elliptic Differential Equation witL Analytic Coefficients Definition of a fundamental solution . . . . . . . . . . . . . . 43 The Cauchy problem . . . . . . . . . . . . . . . . . . . . . 45 Solution of the inhomogeneous equation with a plane wave function as right hand side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 The fundamental solution. . . . . . . . . . . . . . . . . . . . . .

Download or read book Plane Waves and Spherical Means Applied written by John and published by . This book was released on 1955-01-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Plane Waves and Spherical Means Applied to Partial Differential Equations written by Fritz John and published by . This book was released on 1955 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Plane Waves and Spherical Means Applied Equations written by Fritz John and published by . This book was released on 1955 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Plane Waves and Spherical Means Applied to Partial Differential Equations written by Fritz John and published by . This book was released on 1955 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Plane Waves and Numerical Means Applied to Partial Differential Equations written by Fritz John and published by . This book was released on 1955 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Radon Transforms written by Boris Rubin and published by Cambridge University Press. This book was released on 2015-11-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

Download or read book Complex Analysis and Dynamical Systems II written by Lawrence Allen Zalcman and published by American Mathematical Soc.. This book was released on 2005 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers reflecting the conference held in Nahariya, Israel in honor of Professor Lawrence Zalcman's sixtieth birthday. The papers, many written by leading authorities, range widely over classical complex analysis of one and several variables, differential equations, and integral geometry. Topics covered include, but are not limited to, these areas within the theory of functions of one complex variable: complex dynamics, elliptic functions, Kleinian groups, quasiconformal mappings, Tauberian theorems, univalent functions, and value distribution theory. Altogether, the papers in this volume provide a comprehensive overview of activity in complex analysis at the beginning of the twenty-first century and testify to the continuing vitality of the interplay between classical and modern analysis. It is suitable for graduate students and researchers interested in computer analysis and differential geometry. Information for our distributors: This book is co-published with Bar-Ilan University.

Download or read book Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2009-06-13 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.

Download or read book Photoacoustic Imaging and Spectroscopy written by Lihong V. Wang and published by CRC Press. This book was released on 2017-12-19 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Photoacoustics promises to revolutionize medical imaging and may well make as dramatic a contribution to modern medicine as the discovery of the x-ray itself once did. Combining electromagnetic and ultrasonic waves synergistically, photoacoustics can provide deep speckle-free imaging with high electromagnetic contrast at high ultrasonic resolution and without any health risk. While photoacoustic imaging is probably the fastest growing biomedical imaging technology, this book is the first comprehensive volume in this emerging field covering both the physics and the remarkable noninvasive applications that are changing diagnostic medicine. Bringing together the leading pioneers in this field to write about their own work, Photoacoustic Imaging and Spectroscopy is the first to provide a full account of the latest research and developing applications in the area of biomedical photoacoustics. Photoacoustics can provide functional sensing of physiological parameters such as the oxygen saturation of hemoglobin. It can also provide high-contrast functional imaging of angiogenesis and hypermetabolism in tumors in vivo. Discussing these remarkable noninvasive applications and so much more, this reference is essential reading for all researchers in medical imaging and those clinicians working at the cutting-edge of modern biotechnology to develop diagnostic techniques that can save many lives and just as importantly do no harm.

Download or read book Analysis Geometry Number Theory The Mathematics of Leon Ehrenpreis written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 2000 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.

Download or read book The Mathematical Legacy of Leon Ehrenpreis written by Irene Sabadini and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.

Download or read book Geometric Analysis and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2013 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.

Download or read book The Boundary Domain Integral Method for Elliptic Systems written by Andreas Pomp and published by Springer. This book was released on 2006-11-14 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.

Download or read book Dynamic Fracture of Piezoelectric Materials written by Petia Dineva and published by Springer Science & Business Media. This book was released on 2014-01-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic Fracture of Piezoelectric Materials focuses on the Boundary Integral Equation Method as an efficient computational tool. The presentation of the theoretical basis of piezoelectricity is followed by sections on fundamental solutions and the numerical realization of the boundary value problems. Two major parts of the book are devoted to the solution of problems in homogeneous and inhomogeneous solids. The book includes contributions on coupled electro-mechanical models, computational methods, its validation and the simulation results, which reveal different effects useful for engineering design and practice. The book is self-contained and well-illustrated, and it serves as a graduate-level textbook or as extra reading material for students and researchers.

Download or read book Elastic wave propagation in transversely isotropic media written by R.C. Payton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.

Download or read book Ultrasonic Waves in Solid Media written by Joseph L. Rose and published by Cambridge University Press. This book was released on 1999 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the physical principles of wave propagation and relates them to ultrasonic wave mechanics and the more recent guided wave techniques that are used to inspect and evaluate aircraft, power plants, and pipelines in chemical processing. An invaluable reference to this active field for graduate students, researchers, and practising engineers.