Complex Proofs of Real Theorems
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Complex Proofs of Real Theorems: (University Lecture Series)

Complex Proofs of Real Theorems: (University Lecture Series)


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About the Book

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, ""The shortest and best way between two truths of the real domain often passes through the imaginary one.'' Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Muntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Zelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime number theorem. Four brief appendices provide all necessary background in complex analysis beyond the standard first year graduate course. Lovers of analysis and beautiful proofs will read and reread this slim volume with pleasure and profit.

Table of Contents:
Preface Early triumphs Approximation Operator theory Harmonic analysis Banach algebras: The Gleason-Kahane-Żelazko theorem Complex dynamics: The Fatou-Julia-Baker theorem The prime number theorem Coda: Transonic airfoils and SLE Liouville’s theorem in Banach spaces The Borel-Carathéodory inequality Phragmén-Lindelöf theorems Normal families

About the Author :
Peter D. Lax, Courant Institute, New York, NY, USA Lawrence Zalcman, Bar-Ilan University, Ramat Gan, Israel


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Product Details
  • ISBN-13: 9780821875599
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Language: English
  • Returnable: N
  • Weight: 200 gr
  • ISBN-10: 0821875590
  • Publisher Date: 30 Mar 2012
  • Binding: Paperback
  • No of Pages: 90
  • Series Title: University Lecture Series


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