P. D. Lax, L. Zalcman: Complex Proofs of Real Theorems

摘要

(University Lecture Series, Vol. 58.) American Mathematical Society, Providence, Rhode Island, 2012, xi+90 S. ISBN 978-0-8218-7559-9 P/b $ 29,-. The book illustrates in a fascinating way how complex variables can be used to provide elegant and efficient proofs of important results in number theory, algebra, approximation theory, operator theory, harmonic analysis, Banach algebras, fluid dynamics, and statistical mechanics. It can be seen as an extended meditation on Hadamard's dictum "The shortest and best way between two truths of the real domain often passes through the imaginary one."