Complex proofs of real theorems
 Author/Creator
 Lax, Peter D.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xi, 90 p. ; 26 cm.
 Series
 University lecture series (Providence, R.I.) ; 58.
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Available online

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QA331.7 .L39 2012

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QA331.7 .L39 2012
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Contributors
 Contributor
 Zalcman, Lawrence Allen.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 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 FugledePutnam theorem
 3.2. Toeplitz operators
 3.3. A theorem of Beurling
 3.4. Prediction theory
 3.5. The RieszThorin 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 PaleyWiener theorem
 4.5. The Titchmarsh convolution theorem
 4.6. Hardy's theorem
 Chapter 5. Banach algebras: the GleasonKahaneŻelazko theorem
 Chapter 6. Complex dynamics: the FatouJuliaBaker theorem
 Chapter 7. The prime number theorem
 Coda. Transonic airfoils and SLE
 Appendix A. Liouville's theorem in Banach spaces
 Appendix B. The BorelCarathéodory inequality
 Appendix C. PhragménLindelöf theorems
 Appendix D. Normal families.
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Peter D. Lax, Lawrence Zalcman.
 Series
 University lecture series ; v. 58
 ISBN
 9780821875599
 0821875590