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Plane Waves And Spherical Means
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Book Synopsis Plane Waves and Spherical Means by : F. John
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 The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the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. . . . . . . . . . . . . . . . . . . . . .
Book Synopsis Plane Waves and Spherical Means Applied to Partial Differential Equations by : Fritz John
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:
Book Synopsis Plane Waves and Spherical Means by : F. John
Download or read book Plane Waves and Spherical Means written by F. John and published by Springer. This book was released on 1955 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. Explores the decomposition of arbitrary functions into functions of the type of plane waves; Radon transformation; more.
Book Synopsis Spherical Means for PDEs by : Karl K. Sabelfeld
Download or read book Spherical Means for PDEs written by Karl K. Sabelfeld and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-19 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monographs presents new spherical mean value relations for classical boundary value problems of mathematical physics. The derived spherical mean value relations provide equivalent integral formulations of original boundary value problems. Direct and converse mean value theorems are proved for scalar elliptic equations (the Laplace, Helmholtz and diffusion equations), parabolic equations, high-order elliptic equations (biharmonic and metaharmonic equations), and systems of elliptic equations (the Lami equation, systems of diffusion and elasticity equations). In addition, applications to the random walk on spheres method are given.
Book Synopsis Photoacoustic Imaging and Spectroscopy by : Lihong V. Wang
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 1027 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.
Book Synopsis Plane Waves and Spherical Means Applied to Partial Differential Equations by : Fritz John
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:
Book Synopsis Complex Analysis and Dynamical Systems V by : Mark Lʹvovich Agranovskiĭ
Download or read book Complex Analysis and Dynamical Systems V written by Mark Lʹvovich Agranovskiĭ and published by American Mathematical Soc.. This book was released on 2013-06-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Fifth International Conference on Complex Analysis and Dynamical Systems, held from May 22-27, 2011, in Akko (Acre), Israel. The papers cover a wide variety of topics in complex analysis and partial differential
Book Synopsis Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture by : Birgit Bergmann
Download or read book Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture written by Birgit Bergmann and published by Springer Science & Business Media. This book was released on 2011-10-24 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: A companion publication to the international exhibition "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933.
Book Synopsis Conference on Inverse Scattering--Theory and Application by : J. Bee Bednar
Download or read book Conference on Inverse Scattering--Theory and Application written by J. Bee Bednar and published by SIAM. This book was released on 1983-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by : Valery V. Volchkov
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.
Book Synopsis Aeronautical Engineering Review by :
Download or read book Aeronautical Engineering Review written by and published by . This book was released on 1957 with total page 1908 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamental Solutions for Differential Operators and Applications by : Prem Kythe
Download or read book Fundamental Solutions for Differential Operators and Applications written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.
Book Synopsis Complex Analysis and Dynamical Systems II by : Lawrence Allen Zalcman
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.
Book Synopsis Spherical Near-field Antenna Measurements by : Jesper E. Hansen
Download or read book Spherical Near-field Antenna Measurements written by Jesper E. Hansen and published by IET. This book was released on 1988 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the aspects of antenna test ranges, data processing schemes and measurement schemes.
Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Book Synopsis Methods of Mathematical Physics by : Richard Courant
Download or read book Methods of Mathematical Physics written by Richard Courant and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.
Book Synopsis Quarterly of Applied Mathematics by :
Download or read book Quarterly of Applied Mathematics written by and published by . This book was released on 1958 with total page 1334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
