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Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon
edited by Michael Christ, Carlos E. Kenig and Cora Sadosky
University of Chicago Press, 1999
Cloth: 978-0-226-10456-0 | Paper: 978-0-226-10455-3

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC
ABOUT THIS BOOK
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 everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.

In 1996, 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 is essential reading for researchers in these and other related fields.
AUTHOR BIOGRAPHY
Michael Christ is professor of mathematics at the University of California, Berkeley. Carlos E. Kenig is the Louis Block Distinguished Service Professor of Mathematics at the University of Chicago. Cora Sadosky is professor of mathematics at Howard University.
TABLE OF CONTENTS
    Preface
    Introduction
    Michael Christ, Carlos E. Kenig, and Cora Sadosky
    1. Calderón and Zygmund's Theory of Singular Integrals
    Elias M. Stein
    2. Transference Principles in Ergodic Theory
    Alexandra Bellow
    3. A Weak-Type Inequality for Convolution Products
    Alexandra Bellow and Alberto P. Calderón
    4. Transference Couples and Weighted Maximal Estimates
    Earl Berkson, Maciej Paluszynski, and Guido Weiss
    5. Periodic Solutions and Nonlinear Wave Equations
    Jean Bourgain
    6. Some Extremal Problems in Martingale Theory and Ilarmonic Analysis
    Donald L. Burkholder
    7. The Monge Ampere Equation, Allocation Problems, and Elliptic Systems with Affine Invariance
    Luis A. Caffarelli
    8. On a Fourth-Order Partial Differential Equation in Conformal Geometry
    Sun-Yung A. Chang
    9. Riesz Transforms, Commutators, and Stochastic Integrals
    A. B. Cruzeiro and P. Malliavin
    10. An Application of a Formula of Alberto Calderón to Speaker Identification
    Ingrid Daubechies and Stéphane Maes
    11. Analytic Capacity, Cauchy Kernel, Menger Curvature, and Rectifiability
    Guy David
    12. Symplectic Subunit Balls and Algebraic Functions
    Charles Fefferman
    13. Multiparameter Calderón-Zygmund Theory
    Robert A. Fefferman
    14. Nodal Sets of Sums of Eigenfunctions
    David Jerison and Gilles Lebeau
    15. Large-Time Behavior and Self-Similar Solutions of Some Semilinear Diffusion Equations
    Yves Meyer
    16. Estimates for Elliptic Equations in Unbounded Domains and Applications to Symmetry and Monotonicity
    Louis Nirenberg
    17. Asymptotic Expansions for Atiyah-Patodi-Singer Problems
    Robert Seeley
    18. Analysis on Metric Spaces
    Stephen Semmes
    19. Developments in Inverse Problems since Calderón's Foundational Paper
    Gunther Uhlmann
    Remarks Addressed to the Conference
    Alberto P. Calderón
    Contributors
    Index







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