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Complex proofs of real theorems

Author: Peter D Lax; Lawrence Allen Zalcman
Publisher: Providence, R.I. : American Mathematical Society, ©2012.
Series: University lecture series (Providence, R.I.), 58.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter D Lax; Lawrence Allen Zalcman
ISBN: 9780821875599 0821875590
OCLC Number: 767719672
Description: xi, 90 pages : illustrations ; 25 cm.
Contents: Chapter 1. Early triumphs --
1.1. The Basel problem --
1.2. The fundamental theorem of algebra --
Chapter 2. Approximation --
2.1. Completeness of weighted powers --
2.2. The Müntz approximation theorem --
Chapter 3. Operator theory --
3.1. The Fuglede-Putnam theorem --
3.2. Toeplitz operators --
3.3. A theorem of Beurling --
3.4. Prediction theory --
3.5. The Riesz-Thorin convexity theorem --
3.6. The Hilbert transform --
Chapter 4. Harmonic analysis --
4.1. Fourier uniqueness via complex variables (d'après D.J. Newman) --
4.2. A curious functional equation --
4.3. Uniqueness and nonuniqueness for the Radon transform --
4.4. The Paley-Wiener theorem --
4.5. The Titchmarsh convolution theorem --
4.6. Hardy's theorem --
Chapter 5. Banach algebras: the Gleason-Kahane-Żelazko theorem --
Chapter 6. Complex dynamics: the Fatou-Julia-Baker theorem --
Chapter 7. The prime number theorem --
Coda. Transonic airfoils and SLE --
Appendix A. Liouville's theorem in Banach spaces --
Appendix B. The Borel-Carathéodory inequality --
Appendix C. Phragmén-Lindelöf theorems --
Appendix D. Normal families.
Series Title: University lecture series (Providence, R.I.), 58.
Responsibility: Peter D. Lax, Lawrence Zalcman.

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