Huygens' Principle and Hyperbolic Equations

✍ Scribed by Paul Gunther

• Publisher: Academic Press
• Year: 1988
• Tongue: English
• Leaves: 888
• Series: Perspectives in Mathematics
• Category: Library

✦ Synopsis

Huygens Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times.

The book aims to present special nontrivial Huygens operators and to describe their individual properties and to characterize these examples of Huygens operators within certain more or less comprehensive classes of general hyperbolic operators. The materials covered in the book include a treatment of the wave equation for p-forms over a space of constant sectional curvature, the Riesz distributions, the Euler-Poisson-Darboux-equations over a Riemannian manifold, and plane wave manifolds.

Physicists will find the book invaluable.

✦ Table of Contents

Content:
PERSPECTIVES IN MATHEMATICS, Vol. 5, Page ii
Front Matter, Page iii
Copyright, Page iv
Dedication, Page v
PREFACE, Pages xi-xvii
ACKNOWLEDGEMENTS, Page xix
INTRODUCTION, Pages xxi-lvii
CHAPTER I, Pages 1-103
CHAPTER II - RIESZ DISTRIBUTIONS, Pages 105-151
CHAPTER III - THE FUNDAMENTAL SOLUTIONS, Pages 153-228
CHAPTER IV - HUYGENS' OPERATORS, Pages 229-301
CHAPTER V - THE EULER-POISSON-DARBOUX EQUATION, Pages 303-458
CHAPTER VI - TRANSFORMATION THEORY, Pages 459-554
CHAPTER VII - SOME THEOREMS ON HUYGENS' OPERATORS OVER FOUR-DIMENSIONAL SPACE-TIMES, Pages 555-640
CHAPTER VIII - PLANE WAVE MANIFOLDS AND HUYGENS' PRINCIPLE, Pages 641-793
TABLE I - Identities for the Weyl tensor in a four-dimensional pseudo-Riemannian space of signature {+.-,-,-}, Pages 795-797
TABLE II - Moments of order ≤ 4 in four dimensions, Pages 799-801
TABLE III - Some formulas for pp-metrics, Pages 803-804
TABLE IV - Some formulas for plane wave metrics, Page 805
APPENDIX I - METRIC AND CURVATURE IN NORMAL COORDINATES, Pages 807-819
APPENDIX II - WEAK HUYGENS' OPERATORS, Pages 821-824
APPENDIX III - HUYGENS' PRINCIPLE FOR SPIN TENSOR EQUATIONS, Pages 825-829
INDEX, Pages 831-832
BIBLIOGRAPHY, Pages 833-847
Perspectives in Mathematics, Page ibc1