Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about a wide variety of topics in mathematics and its applications, including harmonic analysis, partial differential equations, and complex analysis, as well as in more applied fields such as signal processing, geophysics, and tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.
In 1995, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book will be welcomed by researchers in these and other related fields.
Author(s): Michael Christ, Carlos E. Kenig, Cora Sadosky
Series: Chicago Lectures in Mathematics
Edition: 1
Publisher: University Of Chicago Press
Year: 2001
Language: English
Pages: 373
Tags: Математика;Дифференциальные уравнения;Дифференциальные уравнения в частных производных;
Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents ......Page 7
Preface ......Page 9
Introduction ......Page 10
1. Calderon and Zygmund's Theory of Singular Integrals ......Page 18
2. Transference Principles in Ergodic Theory ......Page 44
3. A Weak-Type Inequality for Convolution Products ......Page 58
4. Transference Couples and Weighted Maximal Estimates ......Page 66
5. Periodic Solutions and Nonlinear Wave Equations ......Page 86
6. Some Extremal Problems in Martingale Theory and Harmonic Analysis ......Page 116
7. The Monge Ampere Equation, Allocation Problems, and Elliptic Systems with Affine Invariance ......Page 134
8. On a Fourth-Order Partial Differential Equation in Conformal Geometry ......Page 144
9. Riesz Transforms, Commutators, and Stochastic Integrals ......Page 168
10. An Application of a Formula of Alberto Calderon to Speaker Identification ......Page 180
11. Analytic Capacity, Cauchy Kernel, Menger Curvature, and Rectifiability ......Page 200
12. Symplectic Subunit Balls and Algebraic Functions ......Page 216
13. Multiparameter Calderon-Zygmund Theory ......Page 224
14. Nodal Sets of Sums of Eigenfunctions ......Page 240
15. Large-Time Behavior and Self-Similar Solutions of Some Semilinear Diffusion Equations ......Page 258
16. Estimates for Elliptic Equations in Unbounded Domains and Applications to Symmetry and Monotonicity ......Page 280
17. Asymptotic Expansions for Atiyah-Patodi-Singer Problems ......Page 292
18. Analysis on Metric Spaces ......Page 302
19. Developments in Inverse Problems since Calderon's Foundational Paper ......Page 312
Remarks Addressed to the Conference ......Page 364
Contributors ......Page 366
Index ......Page 370
