Complex proofs of real theorems /

Complex proofs of real theorems /

Show other versions (1)

Complex analysis has been pushed to the margins of mathematics over the past half century say mathematicians Lax (New York U.) and Zalcman (Bar-Ilan U.). They present an overview for anyone who enjoys analysis and reading pretty proofs, and are familiar with basic functional analysis and some elemen...

Full description

Bibliographic Details
Main Author: Lax, Peter D
Other Authors: Zalcman, Lawrence Allen
Format: Book
Language:English
Published: Providence, R.I. : American Mathematical Society, [2012], ©2012
Providence, R.I. : c2012
Providence, R.I. : [2012]
Series:University lecture series (Providence, R.I.) ; 58
University lecture series ; v. 58
Subjects:
Approximation theory
Functional analysis
Functions of complex variables
Approximations and expansions
Functions of a complex variable
Harmonic analysis on Euclidean spaces
Number theory
Operator theory
Probability theory and stochastic processes
Real functions
Funktionentheorie
Harmonische Analyse
Operatortheorie
Table of 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
  • 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
  • ch. 1 Early triumphs. 1.1. The Basel problem ; 1.2. The fundamental theorem of algebra
  • ch. 2. Approximation. 2.1. Completeness of weighted powers ; 2.2. The Müntz approximation theorem
  • ch. 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
  • ch. 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
  • ch. 5. Banach algebras : the Gleason-Kahane-Żelazko theorem
  • ch. 6. Complex dynamics : the Fatou-Julia-Baker theorem
  • ch. 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.
  • Chapter 1. Early triumphs Chapter 2. Approximation Chapter 3. Operator theory Chapter 4. Harmonic analysis 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

Similar Items