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Books
Complex proofs of real theorems
- Author / Creator
- Available as
- Online
- Physical
Details
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- Creator
- Peter D. Lax, Lawrence Zalcman
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- Providence, R.I. : American Mathematical Society, [2012]
- ©2012
- Physical Details
-
- xi, 90 pages ; 26 cm
- ISBNs
- 0821875590, 9780821884898, 9780821875599, 0821884891
- OCLC
- ocn907358873, ocn767719672
- Includes bibliographical references.
- 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
Subjects
- Functions of complex variables.
- Approximation theory.
- Functional analysis.
- Functions of a complex variable.
Unknown
- Approximations and expansions.
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- Operator theory.
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- Harmonic analysis on Euclidean spaces.
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- Functional analysis.
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- Real functions.
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- Number theory.
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- Probability theory and stochastic processes.
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