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Complex proofs of real theorems / Peter D. Lax, Lawrence Zalcman.

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Author/Creator:
Lax, Peter D.
Language:
English
Imprint:
Providence, R.I. : American Mathematical Society, c2012.
Format:
  • Book
  • xi, 90 p. ; 26 cm.
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 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.
Contributor:
Zalcman, Lawrence Allen.
Series:
University lecture series ; v. 58
University lecture series (Providence, R.I.) ; 58.
Subjects:
ISBN:
9780821875599
0821875590

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