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Fourier Analysis in Several Complex Variables by Leon Ehrenpreis ISBN: 0486449750 Dover Publications Price: $27.95 click here to see this book This text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. It begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis, and then focuses on applications to partial differential equations. The final section explores functions and their role in Fourier representation. Problems. 1970 edition. Unabridged republication of the edition published by John Wiley & Sons, Inc., New York, 1970. Table of Contents for Fourier Analysis in Several Complex Variables 1. Introduction, Analytically Uniform Spaces, and Multiplicity Varieties A. Quotient Structure Theorems 2. The Geometric Structure of Local Ideals and Modules 3. Semilocal Theory 4. Passage from Local to Global 5. Examples B. Systems of Partial Differential Equations with Constant Coefficients 6. Inhomogeneous Equations 7. Integral Representation of Solutions of Homogeneous Equations 8. Extension and Comparison Theorems. Elliptic and Hyperbolic Systems 9. General Theory of Cauchy's Problem 10. Balayage and General Boundary Value Problems 11. Miscellanea C. Sequences of Operators 12. Lacunary Series. Refined Comparison Theorems 13. General Theory of Quasianalytic Functions Bibliography Index of Special Notation Index

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