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 The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the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 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 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 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 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.
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 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
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:
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.
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 On a Variational Approach to the Problems of Propagation of Plane and Spherical Waves written by Willem Stuiver and published by . This book was released on 1959 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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:
Download or read book The Expansion of a Spherical Wave Into Plane Waves written by J. Mathew and published by . This book was released on 1978 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Waves And Distributions written by Jonsson Thordur and published by World Scientific. This book was released on 1995-05-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with an introduction on continuum mechanics and a derivation of the linear partial differential equations for sound waves in fluids and elastic waves in solids. There is a brief chapter on the wave equations of electrodynamics. This is followed by a description of plane wave solutions and a discussion of concepts like reflection, refraction, polarization and the role of boundary conditions.The second part of the book deals with the theory and applications of distributions and Fourier transforms. Furthermore, dispersion, the method of stationary phase, Kramers-Kronig relations and various examples including surface waves on liquids are discussed.This text is unique because it emphasizes the use of distributions to analyze the solutions of the wave equation. The treatment of continuum mechanics is self-contained, as well as the discussion on distributions and Fourier transforms. In addition, many classical methods of theoretical physics are thoroughly discussed, e.g. the use of Green functions and multipole expansions.
Download or read book Fundamentals of Spherical Array Processing written by Boaz Rafaely and published by Springer. This book was released on 2018-09-27 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays, and was written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The new edition includes additions and modifications, and references supplementary Matlab code to provide the reader with a straightforward start for own implementations. The book is also accompanied by a Matlab manual, which explains how to implement the examples and simulations presented in the book. The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. In turn, the third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters highlight various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including those that achieve maximum directivity and maximum robustness are developed, along with the Dolph–Chebyshev beamformer. The final chapter discusses more advanced beamformers, such as MVDR (minimum variance distortionless response) and LCMV (linearly constrained minimum variance) types, which are tailored to the measured sound field. Mathworks kindly distributes the Matlab sources for this book on https://www.mathworks.com/matlabcentral/fileexchange/68655-fundamentals-of-spherical-array-processing.
