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Viser: Plane Waves and Spherical Means Applied to Partial Differential Equations
Plane Waves and Spherical Means Applied to Partial Differential Equations
Fritz John
(2004)
Sprog: Engelsk
Dover Publications, Incorporated
128,00 kr.
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Detaljer om varen
- Paperback: 176 sider
- Udgiver: Dover Publications, Incorporated (September 2004)
- ISBN: 9780486438047
Elementary and self-contained, this heterogeneous 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. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with constant coefficients and the problem of determining a function from its integrals over spheres of radius 1. 1955 edition.
I. Decomposition of an Arbitrary Function into Plane WavesII. The Initial Value Problem for Hyperbolic Homogeneous Equations with Constant CoefficientsIII. The Fundamental Solution of a Linear Elliptic Differential Equation with Analytic CoefficientsIV. Identities for Spherical MeansV. The Theorems of Asgeirsson and HowardVI. Determination of a Function from its Integrals over Spheres of a Fixed RadiusVII. Differentiability Properties of Solutions of Elliptic SystemsVIII. Regularity Properties of Integrals of Solutions over Time-like LinesBibliographyIndex
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