Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon (Chicago Lectures in Mathematics)

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. 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 Alberto P. Caldern (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 Caldern'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. With contributions Elias M. Stein Alexandra Bellow Earl Berkson Maciej Paluszynski Guido Weiss Jean Bourgain Donald L. Burkholder Luis A. Caffarelli Sun-Yung A. Chang A. B. Cruzeiro P. Malliavin Ingrid Daubechies Stphane Maes Guy David Charles Fefferman Robert A. Fefferman David Jerison Gilles Lebeau Yves Meyer Louis Nirenberg Robert Seeley Stephen Semmes and Gunther Uhlmann as well as Caldern's remarks to the assembled conference. Alberto P. Calderon (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 Calderon'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. Presents papers from a February 1996 conference in honor of a leading analyst who helped define the "Chicago school" of analysis. Papers offer syntheses of several major fields of mathematics as well as original research articles. Topics include transference principles in ergodic theory, periodic solutions and nonlinear wave equations, a fourth-order partial differential equation in conformal geometry, and symplectic subunit balls and algebraic functions. Includes an account of Calderon's life and career. This volume originated in papers given at a conference on harmonic analysis and partial differential equations. It presents syntheses of several major fields of mathematics as well as original research articles. At the occasion of the conference in honor of Alberto Calderon's seventy-fifth birthday, it is most fitting that we celebrate the mathematical achievements for which he is so much admired.